PSPM BY CHAPTER

PSPM 2 PAST YEAR QUESTIONS BY TOPIC

TOPIC 1: ELECTROSTATICS

SESSION 2005/2006 SF027/2 No. 2
1. A –2 µC charge lies on the straight line between a 3 µC charge and a 1 µC charge. The

separation between the 3 µC and 1 µC is 4 cm.
(a) Draw the position of the three charges and show the forces acting on the –2 µC

charge.
(b) Calculate the distance of the 3 µC charge from –2 µC charge where net force on –2µC

charge is zero.
[6 marks]

SESSION 2008/2009 SF027/2 No. 10
2.

A +Q 200 V
B 300 V
400 V
C 500 V
600 V

FIGURE 16.1
FIGURE 16.1 represents the equipotential surfaces and electric filed lines near a positive
point charge Q.
(a) From FIGURE 16.1 give three relationships between the equipotential surfaces and

the electric field lines.
(b) Calculate the work done by the electric field on a 3 μC test charge that is displaced

from point
(i) A to B.
(ii) A to C.
(c) If charge Q is 5 nC,
(i) calculate the distance between the point charge Q and A.
(ii) calculate the electric field at A.
(iii) and a new point charge of −5 nC is placed near Q, sketch where this new

charge could be placed such that the potential at A is zero. Explain your
answer.

[10 marks]

1

SESSION 2011/2012 SF026/2 No. 1
3. (a) State Coulomb’s law.

[1 mark]
(b) An amount of charge is transferred from a neutral plastic bead to another identical

neutral bead located 15 cm away. The force of attraction between the beads is
2.0 × 10−4 N. How many electrons were transferred from the first bead to the second?

[4 marks]
(c)

FIGURE 16.2
Two point charges q1  3.00 µC and q2  5.00 µC are placed at the two corners of
a triangle of sides 0.30 m, 0.40 m, and 0.50 m as shown in FIGURE 16.2. P is the
third corner of the triangle. Calculate
(i) the magnitude of the electric field at P.
(ii) the electric potential at P.
(iii) the work needed to bring a test charge from infinity to P.

[10 marks]

SESSION 2012/2013 DF035/2 No. 1 [2 marks]
4. (a) (i) State Coulomb’s Law.

(ii) Define electric potential.

(b)

FIGURE 16.3
Three point charges are located at the corners of an equilateral triangle with sides
0.5 m as shown in FIGURE 16.3.
(i) Sketch the two forces that act on the +3.5 µC charge.
(ii) Calculate the magnitude of each force.

2

(iii) Determine the magnitude and direction of the resultant force on the +3.5 µC
charge.
[13 marks]

SESSION 2012/2013 SF026/2 No. 1 (a) & (b)
5. (a) (i) Define the electric potential V at a point P in an electric field.

(ii) An isolated charge Q = −5×10−6 C is placed in a region and it creates an
electric field around it. Calculate the work done to move a point charge
q = 2.0×10−7 C from point S to point P which is located at 60 cm and 30 cm
respectively from charge Q.
[4 marks]

(b) A

10 cm 10 cm

B˗q 5 cm 5 cm
C

D +2q

FIGURE 16.4

FIGURE 16.4 shows two point charges ˗q and +2q placed at points B and C
respectively. If q = 1.0 x l0˗6 C, calculate
(i) the electric field at the point D.
(ii) the potential energy of all charges when the point charge 2.0x10˗6 C is placed

at A.
[6 marks]

SESSION 2013/2014 DF035/2 No. 1
6. (a) Define

(i) electric field strength.
(ii) electric potential.

[2 marks]
(b)

FIGURE 16.5

FIGURE 16.5 shows two point charges, q1 = – 2 μC and q2 = – 4 μC, placed at 10 cm
and 28 cm from a point P respectively.
(i) Sketch the direction of electric field strength at point P due to the two point

charges.
(ii) Determine the magnitude and direction of the electric field strength at point P.

3

(iii) Calculate the electric potential at point P.
(iv) Calculate the electric potential energy of the system of charges.

[13 marks]

SESSION 2014/2015 DF035/2 No. 1
7. (a) (i) Define the equipotential surface.

(ii) When a charge q moves from one point to another point on an equipotential
surface, will there be any work done on it? Explain your answer.
[3 marks]

(b) q1 q2

q3 q4

20 cm
FIGURE 16.6

FIGURE 16.6 shows four charges, q1, q2, q3, and q4, each of magnitude 4 µC are
placed at the respective corners of a square with sides 20 cm. Calculate the
(i) Electric field at the center of the square.
(ii) Electric force acting on another charge of magnitude – 4 µC placed at the

center of the square.
[6 marks]

(c) Two point charges, each of 2 µC are located at coordinates (0.1, 0) m and (-0.1, 0) m,
respectively. Calculate the
(i) electric potential at coordinate (0, 0.5) m.
(ii) change in the electric potential energy of the system if a third charge of
magnitude -3 µC is brought from infinity to coordinate (0, 0.5) m.
[6 marks]

ANSWERS:
TOPIC 1: ELECTROSTATICS

1. (b) 2.53×10−2 m
2. (b) (i) −3×10−4 J (ii) 0 J (c) (i) 0.15 m (ii) 2000 N C−1
3. (b) 1.475×1011 (c) (i) 2.4×105 NC-1, θ = 36.870 (ii) 0 V (iii) 0 J
4. (b) (ii) 0.252 N (iii) 0.2182 N, 300 below positive x- axis
5. (a) (ii) −0.015 J (b) (i) 1.08×107 N C−1 (ii) 0 J
6. (b) (ii) –1.38×106 N C−1 (iii) –3.086×105 V (iv) 0.189 J
7. (a) (ii) 0 J (b) (i) 0 NC-1 (ii) 0 N (c) (i) 7.06x104 V (ii) -3.18 x10-3 J

4

TOPIC 2: CAPACITOR AND DIELECTRICS

SESSION 2005/2006 SF027/2 No. 10 (a) (iii)
1. Calculate the energy stored if the charge in the capacitor is 1.2 C and the capacitance in the

capacitor is 19.5 pF.
[2 marks]

SESSION 2005/2006 SF027/2 No. 10 (b) [2 marks]
2. A 20 F capacitor has a charge of 240 C is connected to a 50 k resistor. [2 marks]
[2 marks]
(a) Calculate the time constant.

(b) Calculate the initial current.

(c) Sketch a graph of current against time.

SESSION 2008/2009 SF027/2 No. 2
3. A 24 μF capacitor is charged to 180 μC. Calculate the additional energy required to charge

the capacitor to 300 μC.

[3 marks]

SESSION 2009/2010 SF027/2 No. 2
4. (a) Define capacitance.

(b) Why electrical energy can still be stored in a capacitor even though the net charge is
zero?

(c) How to increase the capacitance of air-filled capacitor without changing its
dimension?
[3 marks]

SESSION 2003/2004 SF027/2 No. 2
5.

C3

V1 C1 C2 C4

C5

FIGURE 17.1

In FIGURE 17.1, given C1 = 3 F, C2 = 11 F, C3 = 12 F, C4 = 6 F, and C5 = 9 F.
(a) Calculate the effective capacitance of the circuit.Error! Reference source not found.

(b) If V1 = 12 V, calculate the total charge Q supplied. [3 marks]
5 [1 mark]

SESSION 2012/2013 DF035/2 No. 2 [2 marks]
6. (a) (i) Define capacitance.

(ii) What is the function of a capacitor?

(b)

FIGURE 17.2

FIGURE 17.2 shows a fully charged 5.6 µF capacitor, connected to a 2.0 Ω resistor and
switch. The potential difference across the capacitor is 12.0 V.
(i) Calculate the charge and energy stored in the capacitor.
(ii) Calculate the time constant, of the circuit. Explain the physical meaning of the

value.
(iii) Calculate the time for the charge in the capacitor to reduce to one fourth of its initial

value after the switch is closed.
(iv) Sketch a graph of charge against time after the switch is closed. Indicate the time

constant, of the graph.
[13 marks]

SESSION 2012/2013 SF026/2 No. 1 (c)
7. 10 V

2 µF K1

K2

2 MΩ

FIGURE 17.3

FIGURE 17.3 shows a 2 µF capacitor connected to a 10 V battery, a 2 MΩ resistor and
switches K1 and K2.
(i) Explain in words the meaning of capacitance.
(ii) Calculate the charge of the capacitor when switch K1 is closed and switch K2 is

opened.
(iii) Switch K1 is then opened and switch K2 closed. Calculate the charge in the capacitor,

8.0 s after K2 is closed.
[5 marks]

6

SESSION 2013/2014 DF035/2 No. 2
8. (a) Define capacitance.

(b)

FIGURE 17.4
FIGURE 17.4 shows an arrangement of four capacitors. The voltage across PQ is
15V.
(i) Calculate the effective capacitance.
(ii) Calculate the charge and voltage across the 20 μF capacitor.
(iii) Is the charge on the 6 μF capacitor equals to that on 20 μF capacitor?

Justify your answer with a calculation (if any).
[9 marks]

(c) A 560 μF capacitor is discharged through a 12 kΩ resistor. Calculate the
(i) time constant.
(ii) time taken for the charge to decrease to 50% of the initial value.
[5 marks]

SESSION 2014/2015 DF035/2 No. 2
9. (a) (i) What is meant by time constant?

(ii) Sketch a graph of charge-time, Q-t for charging of a capacitor. Label Qo and
the value of Q at time, t = RC.
[5 marks]

(b) 20 V

C1

C2 C3

FIGURE 17.5
FIGURE 17.5 shows a circuit consists of three capacitors, C1 = 100 µF, C2 =
22 µF, C3 = 47 µF connected to a 20 V battery. Calculate the
(i) effective capacitance of the circuit.

7

(ii) charge stored in the capacitor C1.
(iii) potential difference across the capacitor C2.

[10 marks]

ANSWERS:
TOPIC 2: CAPACITOR & DIELECTRICS

1. 3.7×10−2 J

2. (a) 1 s (b) 2.4×10−4 A
3. 1.2×10−3 J

5. (a) (b) 72 μC

6. (b) (i) 6.72×10-5 C, 4.032×10-4 J (ii) 1.12×10-5 s (iii) 1.56×10-5 s

7. (ii) 2×10-5 C (iii) 2.71×10-6 C
8. (b) (i) 5.95 µF (ii) 8.93×10−5 C, 4.47 V (iii) No (c) (i) 6.72 s (ii) 4.66 s

9. (b) (i) 1.15 x 10-4 F (ii) 2 x 10-2 J (iii) 13.64 V

TOPIC 3: ELECTRIC CURRENT AND DIRECT-CURRENT CIRCUITS

SESSION 2008/2009 SF027/2 No. 3 3Ω
1.

2Ω 4Ω

1Ω
5Ω

FIGURE 18.1

Calculate the effective resistance of the circuit in FIGURE 18.1.

[4 marks]

SESSION 2009/2010 SF026
2. The dimensions of two copper wires P and Q are given in TABLE 1.

Wire Length Radius
P L R
Q 2L R/2

TABLE 1
8

Calculate the ratio of resistance of P and Q.

[3 marks]

SESSION 2011/2012 SF026/2 No. 2
3. (a) State Ohm’s law.

[1 marks]
(b) A potential difference of 15 V is applied across a uniform wire of length 2.80 m and

radius 0.30 cm. If 0.60 A current flows in the wire, calculate

(i) the resistance of the wire.
(ii) the resistivity of the wire.

[3 marks]

(c)

FIGURE 18.2

Two batteries and four resistors are connected in a circuit where currents I1, I2 and I3
flow as shown in FIGURE 18.2.
(i) Calculate I1, I2 and I3.
(ii) What does it imply if the calculated current is negative?
(iii) Calculate the potential difference between points X and Y.
(iv) Calculate the total power dissipated in the circuit.

[11 marks]

SESSION 2011/2012 DF035/2 No. 3
4. (a) (i) Define electric current.

(ii) Sketch a diagram to show the motion of free electrons in a current carrying
wire.

(iii) Current of 0.4 A flows in a light bulb. Calculate the number of electrons that
enter the light bulb every minute.
[7 marks]

(b) A wire of cross-sectional area 0.8 mm2 is connected to a variable voltage, V and the
current, I in the wire is measured. At 27˚C, the resistance of the wire is 0.25 Ω and
the resistivity is 4.5 × 10-8 Ω m.
(i) Calculate the length of the wire.
(ii) Calculate the change in the resistance of the wire when it is heated to 50˚C.
The temperature coefficient of resistivity of the wire is 3.9×10-3˚C-1.
(iii) State the relationship between V and I.

9

(iv) Sketch on the same axes, V-I graph of the wire at temperature 27˚C and 50 ˚C.
[8 marks]

SESSION 2012/2013 DF035/2 No. 4
5. (a) (i) What is a voltage divider?

(ii) Explain the principle of the voltage divider.
(iii) You are supplied with resistors 2Ω, 4 Ω, 6 Ω, a 24 V battery and connecting

wires. Sketch a circuit using all the resistors that can be used to obtain a
voltage of 4 V.

[5 marks]

(b)

FIGURE 18.3

FIGURE 18.3 shows a 2 A current flows into a combination of four resistors.

Calculate

(i) the equivalent resistance of the combination.
(ii) the current that flows in the 3 Ω resistors.
(iii) the power dissipated by the 12 Ω resistor.

[10 marks]

SESSION 2012/2013 DF035/2 No. 1 [2 marks]
6. (a) State Kirchhoff’s laws.

(b)

FIGURE 18.4
10

FIGURE 18.4 shows a circuit containing three batteries and three resistors.
(i) Calculate I1, I2 and I3.
(ii) Calculate the potential difference between points P and Q. Which point has

the higher potential?
[9 marks]

(c)

FIGURE 18.5
* FIGURE 18.5 shows a Wheatstone bridge in equilibrium condition. The emf of the
battery is 2 V and the internal resistance, r is 0.5 Ω.
(i) What is the reading of the galvanometer G?
(ii) Calculate the resistance R.
(iii) What will happen to the value of R, If the internal resistance of the

battery increases?
SESSION 2012/2013 SF026/2 No. 2
7. (a) (i) Define the emf of a battery.

(ii) A battery has an emf of 12 V and internal resistance r is connected to a
resistor R = 4 Ω. The voltage across the battery terminal is measured to be 8
V. Calculate the internal resistance.
[3 marks]

(b)

FIGURE 18.6

11

FIGURE 18.6 shows a circuit consisting of batteries with internal resistance 6 V, 1 Ω
and 10 V, 2 Ω and connected to resistors of 8 Ω, 9 Ω and 12 Ω. By using the anti-
clockwise loop as shown, calculate
(i) the current that flows through the 8 Ω resistor.
(ii) the potential difference between point A and C, VAC

[6 marks]
(c) The heating element is made of 1.0 m long wire with cross-sectional area of 3.1×l0−6

m2. The wire has a resistivity of ρο = 6.8×l0−5 Ω m at a temperature
Tο = 320º C and a temperature coefficient of resistivity α = 2.0 x l0−3 K−1.
(i) Define temperature coefficient of resistivity, α.
(ii) Determine the resistance of the heating element at an operating temperature of

420°C.
(ii) If the heating element is connected to 100 V power supply, is the power

dissipated at 320°C and 420°C are the same? Justify your answer.
[6 marks]

SESSION 2013/2014 DF035/2 No. 3
8. (a) Describe microscopic model of current.

[3 marks]
(b) The current in a wire is 2.0 mA. In 2.0 ms,

(i) how much charge flows through a point in the wire, and
(ii) how many electrons pass the point?

[4 marks]
(c) A resistor made of carbon rod has uniform cross-sectional area of 5.0 mm2. When a

potential difference of 15.0 V is applied across the ends of the rod, the rod carries a
current of 4.0 mA. The resistivity of carbon is 3.5 x 10-5 Ω m. Calculate the
(i) resistance of the rod.
(ii) length of the rod.

[4 marks]
(d) A copper wire is initially at 25.0oC. What is the final temperature of the wire if its

resistance is increased by 20%? Temperature coefficient of resistivity for copper, α =
6.8 x 10-3 oC-1.

[4 marks]

SESSION 2013/2014 DF035/2 No. 4
9. (a) (i) Define emf.

(ii) Explain the source of internal resistance in a battery.
[3 marks]

(b) A battery of emf 15.0 V has a terminal voltage of 11.6 V when connected to an
external load resistor R. If 12.5 W is delivered, calculate the
(i) resistance R.
(ii) internal resistance of the battery.
[6 marks]

(c) FIGURE 18.7 shows a combination of four resistors connected to 12 V battery.
Calculate
(i) the equivalent resistance of the resistors.

12

(ii) the current I.

[6 marks]

5.0 Ω

2.0 Ω 7.0 Ω 9.0 Ω

12 V

I [2 marks]
FIGURE 18.7

SESSION 2013/2014 DF035/2 No. 5
10. (a) State the two Kirchhoff’s Law.

(b) R1 = 15 Ω

V1 = 6.0 V R2 = 20 Ω I1
P I2

Q

I3
V2 = 9.0 V

FIGURE 18.8

FIGURE 18.8 shows a circuit containing two batteries and two resistors. Determine
the
(i) current I1, I2, and I3.
(ii) potential difference across P and Q.

[8 marks]
(c) (i) What is the function of a potential divider?

(ii)

FIGURE 18.9
FIGURE 18.9 shows a potential divider consisting of a wire XY of length 1.0
m and resistance 5.0 . A cell of emf 2.0 V with internal resistance o.5  is

13

connected in series with a 3.0 . When another cell with  is connected to the
potential divider, the balance length XQ is 76.2 cm. Calculate .

[5 marks]

SESSION 2014/2015 DF035/2 No. 3 [3 marks]
11. (a) (i) Sketch a voltage-current, V-I graph for an ohmic conductor. [4 marks]

(ii) What does the slope of the V-I graph represent?

(b) A 100 W and 75 W light bulbs are connected to the same voltage source.
(i) Which bulb draws a larger current? Explain your answer.
(ii) Which bulb has a higher resistance? Explain your answer.

2Ω
(c)

10 V 1Ω 4Ω 3Ω

5Ω
FIGURE 18.10
FIGURE 18.10 shows a circuit consists of resistor connected to a 10 V battery.
Calculate the
(i) Effective resistance of the circuit.
(ii) Power delivered by the battery.

[8 marks]
SESSION 2014/2015 DF035/2 No. 4
12. (a) (i) Why does the resistance of a metal wire increases with temperature?

(ii) What is a superconductor?
(iii) How does the temperature influence the conductivity of a superconductor?

[4 marks]
(b) (i) Define temperature coefficient of resistivity.

(ii) The resistivity of a material at 320 ˚C is 6.8×10-5 Ω m. Calculate resistivity of
material at 450 ˚C if the temperature coefficient of resistivity is 2.3×10-3 ˚C-1.
[4 marks]

(c) FIGURE 18.11 shows a circuit of a 5.0 Ω resistor connected in series with a battery.
S

V 5Ω

FIGURE 18.11
14

A voltmeter connected across the battery gives a reading of 3.5 V and 2.9 V when the
switch S is opened and closed respectively.
(i) Why does the voltmeter reading drop when the switch S is closed?

(ii) Determine the internal resistance of the battery.
(iii) What is the reading of the voltmeter if a conducting wire is connected

momentarily across the 5.0 Ω resistor while switch S is closed?
[7 marks]

SESSION 2014/2015 DF035/2 No. 5
13. (a) * With the help of a circuit diagram, explain how a Wheatstone Bridge is used

to determine the resistance of an unknown resistor.
[4 marks]

I1 I3

(b)

12 V

240 Ω 560 Ω

128 Ω

6 V I2

100 Ω 24 V

FIGURE 18.12

For the circuit in FIGURE 18.12, calculate the current I1, I2 and I3.

[8 marks]

(c)

220 V x=1
x=0

FIGURE 18.13
FIGURE 18.13 shows a light dimmer consisting of a 150 Ω variable resistor, 220 V
voltage source and a light bulb. The slider moves between x = 0 to x = 1. If it is at
x = 0.3, calculate the voltage of the bulb.

[3 marks]

15

ANSWERS:

TOPIC 3: ELECTRIC CURRENT AND DIRECT-CURRENT CIRCUITS

1. 2.45 Ω

2. RP  1
RQ 8

3. (b) (i) 25 Ω (ii) 2.52×10-4 Ω m (c) (i) -1.846 A, -0.231 A, 1.616 A
(iii) 4.16 V (iv) 20.763 W

4. (a) (iii) 1.5×1020 electrons (b) (i) 4.44 m (ii) 2.58 Ω
5. (b) (i) 6.3 Ω (ii) 1.4 A (iii) 4.32 W
6. (b) (i) – 2.26 A, 2.96 A, 0.69 A (ii) 6.16 V (c) (i) 0 V (ii) 0.12 Ω

(iii) Remain unchanged
7. (a) (ii) 2 Ω (b) (i) 0.5 A (ii) 5.5 V (c) (ii) 26.33 Ω
8. (b) (i) 4×10-6 C (ii) 2.5×1013 electrons (c) (i) 3.75×103 Ω (ii) 535.7 m

(d) 29.41oC
9. (b) (i) 10.76 Ω (ii) 3.154 Ω (c) (i) 1.634 Ω (ii) 7.34 A
10. (b) (i) 1 A, 0.45 A, 1.45 A (ii) 9 V (c) (ii) 0.899 V
11. (b) (i) 100 W bulb draws a larger current (ii) 75W bulb has a higher resistance

(c) (i) 0.878 Ω (ii) 113.9 W
12. (b) (ii) 8.87x10-5 Ωm (c) (ii) 1.034 Ω (iii) 3.5 V

13. (b) I1 = 0.03 A, I2 = 0.07 A, I3 = - 0.05 A (c) 66.15 V

TOPIC 4: MAGNETISM

SESSION 2005/2006 SF027/2 No. 4
1. × × × × × × ×

B
× × × × × ×B×
×××××××

×××××××

FIGURE 19.1

A copper rod of mass 0.08 kg and length 0.20 m is attached to two thin current carrying

wires, as shown in FIGURE 19.1. The rod is perpendicular to a uniform magnetic field of

0.60 T. Determine the magnitude and the direction of the electric current to keep the copper

rod fixed and stay horizontal. 1

[3 marks]

16

SESSION 2005/2006 SF027/2 No. 11 (c)
2. A rectangular coil of 30 turns has a dimension of 1.0 cm × 1.5 cm. The coil experiences a

torque of 3.3×10-4 N m when placed in a magnetic field of 0.35 T. What is the current in the
coil?

[2 marks]
SESSION 2008/2009 SF027/2 No. 4
3.

FIGURE 19.2
FIGURE 19.2 shows two long parallel wires, each carrying a 5 A current in opposite
direction. Determine the magnetic field, B at point P, 3 cm from both wires.

[4 marks]

SESSION 2010/2011 SF027/2 No. 12
4. (a) A 4 cm × 8 cm rectangular coil with 120 turns carrying 0.5 mA current is placed in a

uniform magnetic field 0.6 T. Calculate the required torque to hold the coil’s plane
parallel to the field.

[3 marks]
(b) A 1.35×10-15 kg particle of charge 5 nC and velocity 3500 m s-1 enters a region of

uniform magnetic field 0.25×10-2 T perpendicular to the field.
(i) Calculate the radius of the path of the particle.
(ii) Explain whether there is any change in the particle’s path when the magnetic

field is reduced half and the particle’s velocity is increased four times.
[5 marks]

(c) A 3.0 cm diameter wire coil with 25 turns and resistance 0.015 Ω is placed coaxially
inside a solenoid. The solenoid with diameter 6 cm, length 26 cm and 1000 turns
carries a transient current 14 A s-1.
(i) Calculate the maximum flux passing through the coil.
(ii) Calculate the current induced in the coil.
(iii) What is the effect on the induced current if the coil is slightly stretched?
Explain your answer.
[7 marks]

SESSION 2011/2012 SF026/2 No. 3
5. (a) Define one ampere.

[2 marks]

17

(b)

FIGURE 19.3

A proton moving at 7.0 x 106 m s-1 along the x- axis enters a region of uniform
magnetic field of magnitude 1.8 T. The direction of the magnetic field is 300 with the
x- axis and parallel to the xy- plane as shown in FIGURE 19.3.
(i) Determine the magnitude and direction of the magnetic force on the proton.
(ii) If the proton is replaced by an electron moving at the same velocity, compare

the magnetic force on the electron to that of the proton. Explain your answer.
(iii) Does the speed of the proton be affected by the magnetic field? Explain your

answer.
[9 marks]

(c) A 40 m electric cable carries a current of 28 A from west to east. The earth magnetic
field is 50 µT, horizontal and directed from south to north. Determine
(i) The magnitude and direction of the magnetic force on the cable.
(ii) The magnetic force on the cable if it is parallel to the direction of the magnetic
field.
[4 marks]

SESSION 2012/2013 DF035/2 No. 6 [2 marks]
6. (a) (i) Define magnetic field.

(ii) Sketch the magnetic field lines of the earth.

(b)

FIGURE 19.4

A wire is bent and placed in a uniform magnetic field B. Current flows in the wire
shown in FIGURE 19.4. Determine the magnitude and direction of the force that acts
on each segment PQ, QR and RS.

18

[6 marks]
(c) The length of a 500 turn solenoid is 3 cm. Calculate the magnetic field intensity

inside the solenoid when it carries a 0.6 A current.
[3 marks]

(d) A particle with a charge of 4.8×10-19 C enters a uniform magnetic field with a velocity
of 2.0×105 m s-1 perpendicular to the field. Calculate the force that exerts on the
particle if the magnitude of the field is 1.5 T.
[3 marks]

SESSION 2012/2013 DF035/2 No. 7
7. (a) (i) Sketch the magnetic field lines around a long current carrying conductor.

(ii) Sketch the resultant magnetic field lines around two parallel long conductors
that carry a current in opposite directions. Explain, in terms of magnetic field
lines, why the force between the wires is repulsive.
[5 marks]

(b) Two long parallel wires, P and Q are fixed on a horizontal plane north- south
direction. Wire P is 10 cm left of Q. Wire P carries 40 A current northwards while
wire Q carries 20 A current southwards. Determine the magnitude and direction of

(i) the resultant magnetic field at midpoint between the wires.
(ii) the resultant magnetic field at a point on the horizontal plane, 8.0 cm from

wire Q.
(iii) the magnetic of force per unit length.

[8 marks]
(c) A 100 turn coil of mean cross-sectional area 15 cm2 carries 2.4 A current. Calculate

the maximum torque on the coil when it is placed in a 0.8 T magnetic field.
[8 marks]

SESSION 2012/2013 SF026/2 No. 3
8. (a)

FIGURE 19.5
FIGURE 19.5 shows a long straight wire carrying a current of I1 = 4.0 A is placed to
the left of a circular loop. The loop has a diameter of d = 0.04 m and carrying a
current of I2 = 2.0 A. Determine the magnitude and direction of the net magnetic field
at the center of the loop.

[7 marks]

19

(b)

FIGURE 19.6
FIGURE 19.6 shows a proton with a speed of 2.2×10 m s-1 entering a region of a
uniform magnetic field between two plates. The plates are separated by a distance of
0.18 m.
(i) Determine the direction of the magnetic force on the proton and sketch its

trajectory when it enters the region between the plates.
(ii) What is the maximum magnitude of the magnetic field so that the

proton does not hit the opposite plate?
[8 marks]

SESSION 2013/2014 DF035/2 No. 6
9. (a) Sketch a labelled diagram of the Earth magnetic field.

[3 marks]
(b) FIGURE 19.7 shows a proton carrying a charge of 1.6×10-19 C entering

perpendicularly a large uniform magnetic field 0.5 T with velocity 2×105 m s-1.
(i) Calculate the magnetic force acting on the proton.
(ii) Sketch the path of the proton in the magnetic field. Explain your

answer.

FIGURE 19.7
[5 marks]

(c)

FIGURE 19.8
20

FIGURE 19.8 shows a current carrying wire with length 0.7 m and mass 80 g placed
horizontally with respect to the floor in a uniform magnetic field of 2 T.
(i) Sketch the forces required to balance the wire.
(ii) Determine the direction of current.
(iii) Calculate the current required to balance the wire.

[7 marks]

SESSION 2013/2014 DF035/2 No. 7 [1 mark]
10. (a) Define one ampere.

(b)

FIGURE 19.9

FIGURE 19.9 shows two long parallel current-carrying conductors separated by 10.0
cm. Determine the
(i) magnetic field created by wire 1 on wire 2.
(ii) force per unit length on wire 2.

[6 marks]
(c) A 20 turn circular coil has a diameter of 30.0 cm and carrying 2.00 A current placed

in a 1.5 T uniform magnetic field.
(i) Determine the maximum torque on the coil.
(ii) Does the maximum torque change if the circular coil is replaced with a square

coil having the same area, number of turns, and current as the circular coil?
Explain your answer.

[5 marks]
(d) In a velocity selector, a proton moves in a circle of radius 5.0 cm in a 0.60 T uniform

magnetic field. Determine the electric field such that the proton moves in a straight
path (undeflected).

[3 marks]
SESSION 2014/2015 DF035/2 No. 6
11. (a) Sketch the magnetic field lines of a

(i) current carrying straight wire.
(ii) current carrying circular loop.

[4 marks]

21

(b)
8A

4 cm 12 cm
5A

FIGURE 19.10

FIGURE 19.10 shows a vertical straight wire inside a horizontal single loop. The
radius of the loop is 12 cm and the wire is 4 cm from the loop. The currents in the
wire and the loops are 8 A and 5 A, respectively. Determine the magnitude and
direction of the resultant magnetic field at the centre of the loop.

[6 marks]
(c) An electron is accelerated through a 100 V potential difference before

perpendicularly entering a uniform magnetic field. Inside the field, the electron
moves in a circular trajectory of radius 4 cm. Calculate the
(i) energy of the electron in joule.
(ii) centripetal force that acts on the electron.
(iii) magnitude of the magnetic field.

[5 marks]

SESSION 2014/2015 DF035/2 No. 7
12. (a) State two magnetic field sources.

[2 marks]
(b) Two long parallel wires, each carries current I, are separated by a distance r.

Determine the magnetic field midway between those two wires in terms of I and r, if
the currents are
(i) in opposite direction, and
(ii) in the same direction.

[5 marks]
(c) A 2.0 m long wire is made into a plane coil of five turns. If the currents in the wire is

30 mA,
(i) calculate the magnetic field at the centre of the coil.
(ii) show the direction of the magnetic field by a simple sketch.

[4 marks]
(d)

v XXX
M
XXX
Nv
B

XXX

FIGURE 19.11

X 2X2 X X

FIGURE 19.11 shows two particles M and N with charges +e and -e respectively
enter a uniform magnetic field B = 0.8 T with the same velocity v = 1.5 x 106 m s-1
(i) Copy FIGURE 8, sketch and label the path of each particles as it enters the

region of uniform magnetic field, and

(ii) determine the magnitude of magnetic force on each particle.
[4 marks]

ANSWERS:
TOPIC 4: MAGNETISM

1. 6.54 A (to the right)

2. 0.21 A

3. 6.67×10-5 T
4. (a) 1.15×10-4 N m (b) (i) 0.378 m (ii) r’ = 8r (c) (i) 4.8×10-5 Wb (ii) 0.08 A
5. (b) (i) 1.008×10−12 N (ii) 1.008×10-12 N (c) (i) 0.056 N (upward) (ii) 0 N

6. (b) PQ = 0.036 N (out of page), QR = 0 N, RS = 0.07 N (into the page)

(c) 0.013 T (d) 1.44×10-13 N

7. (b) (i) 2.4×10-4 T (into the page) (ii) −5.56×10−6 T (out of page)
(iii) 1.6×10−3 N m (c) 0.288 N m

8. (a) −2.28 x 10-5 T (into the page) (b) (ii) 0.128 T

9. (b) (i) 1.6×10-14 N (c) (ii) to the left (iii) 0.56 A
10. (b) (i) 1×10-5 T (ii) 8×10-5 N m-1 (c) (i) 4.24 N m (d) 1.7×106 N C-1

11. (b) 0.62x10-5 T (out of the page) (c) (i) 1.6x10-17 J (ii) 8x10-16 N (ii) 8.43x10-4 T

12. (b) (i) (2x107 )  (I1  I 2 )  (ii) (2x107 ) I2  I1  (c) (i) 1.48 x10-6 T
r  r

(d) (ii) FM = FN = 1.92 x 1013 N

TOPIC 5: ELECTROMAGNETIC INDUCTION

SESSION 2005/2006 SF027/2 No. 5

1. An AC generator consists a coil of 30 turns with cross sectional area 0.05 m2 and resistance
100 . The coil rotates in a magnetic field 0.50 T at a frequency of 20.0 Hz. Calculate
(a) the maximum induced emf.
(b) the maximum induced current.
[4 marks]

SESSION 2005/2006 SF027/2 No. 12

2. (a) A 400-turn solenoid has a cross-sectional area 1.81103 m2 and length 20 cm
carrying a current of 3.4 A.
(i) Calculate the inductance of the solenoid.
(ii) Calculate the energy stored in the solenoid.
(iii) Calculate the induced emf in the solenoid if the current drops uniformly to
zero in 55 ms.

23

(iv) Explain why a spark jumps across the contact of a switch when the switch is
disconnected.
[8 marks]

SESSION 2006/2007 SF027/2 No. 4

3. A metal rod moves perpendicularly through a 1.5 T uniform magnetic field at a speed of 2
cm s-1. If the length of the rod is 40 cm and the resistance is 3 Ω. Calculate
(a) the induced emf
(b) the induced current.
[4 marks]

SESSION 2006/2007 SF027/2 No. 12 (b) & (c)

4. (a) (i) State Lenz’s law

(ii)

FIGURE 20.1
The solenoid in FIGURE 20.1 is moved at constant velocity towards a fixed bar
magnet. Using Lenz’s Law, determined the direction of the induced current through
the resistor. Explain your answer.

[4 marks]
(b) A 500-turn AC generator coil of cross-sectional area 3 × 10-2 m2 is rotated at a rate of

1500 rpm in a uniform magnetic field of 2.5 × 10-3 T.
(i) Calculate the peak value of the induced emf.
(ii) Calculate the rms value of the induced emf.

[5 marks]
SESSION 2007/2008 SF027/2 No. 4

5. A coil has an inductance of 45 mH and a resistance 0.3 Ω. An emf of 12 V is applied to the
coil until equilibrium current is achieved.
(a) Calculate the energy stored in the coil.
(b) State the change in the stored energy if the number of turns in the coil is increased.
[4 marks]

SESSION 2007/2008 SF027/2 No. 12 (b)

6. A 300-turn solenoid of length 25 cm has a cross-sectional area of 15 cm2. A current of 8 A
flows through the solenoid. Calculate
(i) the magnetic field at the axis of the solenoid.

24

(ii) the total flux linkage passing through the solenoid.
(iii) the self-inductance of the solenoid.
(iv) the energy stored in the solenoid.

[8 marks]

SESSION 2008/2009 SF 027/2 No. 12

7. A coil of inductance L carrying a steady current I has an energy U.
(i) Show that U =½ LI2.

(ii) Where is the energy being stored?

[5 marks]

SESSION 2010/2011 SF 027/2 No. 4

8. A 600 turns solenoid is 0.01 m long. When the current is increased from 0 to 3 A in 0.4 s, the
induced emf is 0.015 V. Calculate the solenoid
(a) inductance.
(b) cross-sectional area.
[4 marks]

SESSION 2010/2011 SF 027/2

9. (a) State Lenz’s law.
(b)

FIGURE 20.2

FIGURE 20.2 shows two coil wrapped around soft iron core. When the current I in
coil A is decreasing, determine the direction of the induced current in coil B. Explain
your answer.

[4 marks]
SESSION 2011/2012 SF026/2 No. 4

10. (a) (i) Define magnetic flux.
(ii) State faraday’s law of magnetic induction.
[2 marks]

(b) The plane of a coil of radius 0.20 m is parallel to the yz-plane in a uniform magnetic
field. The magnetic field is 0.40 T and in the positive x- direction.
(i) Calculate the magnetic flux through the coil.
(ii) The coil is then rotated clockwise about the y-axis, such that the normal of the
coil is now 300 with respect to the x-axis. Calculate the average induced emf
in the coil if the time taken for the rotation in 0.50 s.
[5 marks]

25

(c) A current of 5.0 A flows in a 400 turn solenoid that has a length of 30.0 cm and cross-
sectional area of 2.00 x 10-4 m2. Calculate
(i) The inductance of the solenoid.
(ii) The energy stored in the solenoid.

(iii) The induced emf in the solenoid.
(iii) The induced emf in the solenoid if the current in the solenoid decreases

uniformly to zero in 0.20 s.
[8 marks]

SESSION 2012/2013 DF035/2 No. 8

11. (a) (i) State the Faraday’s law for electromagnetic induction. [2 marks]
(ii) State Lenz’s law.

(b)

FIGURE 20.3
A metal rod is free to slide on horizontal conducting rails that are connected to a 5 Ω
resistor as shown in FIGURE 20.3. The system lies in a uniform magnetic field
B = 0.16 T pointing vertically downwards. The rod is moved with constants velocity,
v = 3 m s−1 to the right.
(i) Determine the direction of the induced current.
(ii) Calculate the force needed to move the rod.

[8 marks]
(c) The length and mean cross-sectional area of a 200 turn coil are 3.5 cm and 0.8 cm2

respectively. A current of 4.0 A flows in the coil.
(i) Calculate the self-inductance of the coil.
(ii) Calculate the average induced emf developed across the coil if the current

supply is switch off with the current reduced to zero in 5 µs.
(iii) What is the effect of the emf calculated in questions (c) (ii) above to the

switch?
[5 marks]

SESSION 2012/2013 SF026/2 No. 4

12. (a) A circular coil of N turns and radius r is rotated at constant frequency f in a uniform
magnetic field B. The magnetic flux linkage of the coil is given by
ϕ = Nπr2B cos (2rf t)
(i) Deduce the expression for e.m.f induced in the coil.
(ii) If N = 100 turns, r = 5 cm, B = 1.0 T and f = 50 Hz, calculate the
maximum emf generated.

26

(iii) A rotating coil generates a maximum emf of 500 V. Calculate the
number of turns if the radius is 5 cm and rotates at the same frequency.

[7 marks]

(b) A solenoid of length / = 10 cm, radius r = 2 cm has 1000 turns.
(i) The current of the solenoid is lowered from 5 A to 0 A within 0.3 s. Calculate
the magnitude of emf induced in the solenoid.
(ii) A second coil with 50 turns is wound coaxially with the solenoid.
Calculate the mutual inductance between the two.
(iii) What is the induced voltage ratio of the coil to the solenoid?
[8 marks]

SESSION 2013/2014 DF035/2 No. 8

13. (a) Define
(i) magnetic flux.
(ii) self-inductance.

[2 marks]

(b)

FIGURE 20.4

FIGURE 20.4 shows a 30 cm rod PQ moving at velocity, v = 45 m s-1 across a
uniform magnetic field 0.8 T.
(i) Calculate the induced emf.
(ii) Determine the induced current and its direction if the resistance in the rod is

15 Q.
(iii) Will emf be induced in the rod if it moves parallel to the magnetic

field? Explain your answer.
[7 marks]

(c) A solenoid of length 30 cm and diameter 4.5 cm has 150 turns. The current that flows
through the solenoid is 1.2 A. Calculate the
(i) self-inductance of the solenoid.
(ii) energy stored in the solenoid.
(iii) mutual inductance of the solenoid when another 250 turns coil is
wound around it.
[6 marks]

27

SESSION 2014/2015 DF035/2 No. 8

14. (a) (i) Explain how emf is induced in a coil.
(ii) What is meant by self-inductance?
[4 marks]

(b) A 400 turns coil is rotating at 3000 rpm in a uniform 0.75 T magnetic field. The
cross-sectional area of the coil is 5 cm2. Calculate the maximum emf generated in the
coil.
[3 marks]

(c) A steady current of 2 A in a coil of 400 turns causes a flux linkage of 10-4 Wb.
Calculate the
(i) average induced emf in the coil if the current reduces to zero in 0.08 s.
(ii) inductance of the coil.
(i) energy stored in the coil.
[6 marks]

(d) Two coaxial solenoids, P and Q have 400 and 700 turns, respectively. A current of
3.5 A flows in coil P produces an average flux of 300 μWb through each turn of coil
P and an average flux of 90 μWb through each turn of coil Q. Calculate the mutual
inductance of the two solenoids.
[2 marks]

ANSWERS:
TOPIC 5: ELECTROMAGNETIC INDUCTION

1. (a)  max  94.2 V(b) I max  0.942 A

2. (a) (i) 1.82×10−3 H (ii) 1.05×10−2 J (iii) 0.113 V
3. (a) 12 mV (b) 4 mA
4. (b) (i) 5.89 V (ii) 4.16 V
5. (a) 36 J
6. (i) 0.0121 T (ii) 5.45×10-3 Wb (iii) 6.81×10-4 H (iv) 2.18×10-2 J
8. (a) 2×10-3 H (b) 4.42×10-5 m2
10. (b) (i) 0.05027 Wb (ii) −0.0136 V (c) (i) 1.34×10-4 H (ii) 1.68×10-3 J (iii) 0 V (iv)

3.35×10-3 V
11. (b) (i) Anticlockwise (ii) 0.015 l2 N (c) (i) 1.15×10-4 H (ii) 92 V

12. (a) (i)   N r2B2 f sin 2 ft  (ii) 246.74 V (iii) 202.64 turns

(b) (i) 0.263 V (ii) 7.896×10-4 H (iii) 0.0502
13. (b) (i) 10.8 V (ii) 0.72 A, from Q to P (c) (i) 9.99×10-7 H (ii) 5.99×10-7 J

(c) (i) 9.99×10−7 H (ii) 5.99×10−7 J (iii) 2.498×10-4 H
14. (b) 47.12 V (c) (i) 0.5 V (ii) 2.0x10-2 H (iii) 4.0x10-2 J (d) 1.80x10-2 H

28

TOPIC 6: ALTERNATING CURRENT

SESSION 2005/2006 SF027/2 No. 12 (c)
1. An a.c. current with r.m.s. voltage 240 V is connected to an RC circuit. The r.m.s. current in

the circuit is 1.5 A and leads the voltage by 60.
(a) Draw a phasor diagram for the RC circuit.
(b) Calculate the value of resistance, R.

[4 marks]

SESSION 2008/2009 SF027/2 No. 5 5A
2. V

20 V

10 V

0.02 s t (s)

FIGURE 21.1

FIGURE 21.1 shows the variation of current and voltage against time in a circuit.
(a) Sketch the current and voltage phasor diagram.
(b) Calculate the power delivered to the circuit.

[4 marks]

SESSION 2009/2010 SF027/2 No. 5

3. (a) (i) Why do average values of alternating voltage and alternating current give

very little information about their actual behaviour?

(ii) Why does root mean square current useful?

(b) Calculate the peak voltage of an electric circuit if it is connected to a 240 V AC source.

[4 marks]

SESSION 2009/2010 SF027/2 No. 12
4. (a) Why an ideal LC circuit does not consume any power?

(b) How do the resistance, capacitive reactance and inductive reactance change when the
frequency in a circuit is decreased? Explain your answer.

(c) A circuit is made up of a 3200 pF capacitor connected in series to a 30 H coil of
resistance 4 . Calculate
(i) impedance at frequency 30 kHz.
(ii) resonant frequency.

(d) The current in an AC circuit lags the voltage by 45. Determine the circuit
components. Explain your answer.

29

[15 marks]

SESSION 2010/2011 SF027/2 No. 1 & 2
5. An a.c current with r.m.s. voltage 240 V is connected to an RC circuit. The r.m.s. current in

the circuit is 1.5 A and leads the voltage by 60.
(a) Draw a phasor diagram for the RC circuit.
(b) Calculate the value of resistance, R.

[4 m]
6.

FIGURE 21.2 [4 marks]
FIGURE 21.2 shows the graph of an alternating current.
(a) Write down the current equation.
(b) Calculate the rms current value.

SESSION 2011/2012 SF026/2 No. 5
7. (a)

FIGURE 21.3
An AC source has an output voltage of V  300sint . The source is connected to a
120 Ω resistor as in FIGURE 21.3.
(i) Calculate the rms voltage.
(ii) Calculate the rms current in the resistor.
(iii) Calculate the average power delivered to the circuit.
(iv) What is the rms voltage if the frequency is doubled?

[7 marks]
(b) An AC source that has a peak voltage of 120 V and frequency of 50.0 Hz is

connected in series to a 900 Ω resistor, a 2.40 H inductor and 10.0 µF capacitor.
Calculate
(i) the impedance of the circuit.
(ii) the phase angle of the circuit.
(iii) the power factor of the circuit.

[8 marks]

30

SESSION 2012/2013 SF026/2 No. 5 (a) & (b)
8. (a) In an AC circuit, the supply voltage is given by V = 240 sin (5000t + π/2) where V in

volt and the current is given by I = 0.480 sin (5000t) where I in ampere and t in
second.

(i) What is meant by root mean squared (rms) value of the current?
(ii) Calculate the impedance of the circuit.
(iii) Sketch the phasor diagram for V and I and state the electrical component(s).

Give your reason.
(iv) Calculate the instantaneous and maximum power dissipated in the circuit.

[9 marks]
(b) A resistor of 6 Ω, a capacitor of 3000 µF and an inductor of 5 mH are connected in

series. If an AC source of 50 Hz and peak voltage of 240 V is connected to this circuit

combination, calculate
(i) The total impedance of the circuit.

(ii) The resonance frequency of the circuit and explain the energy dissipated
during the resonance.
[6 marks]

SESSION 2012/2013 DF045 No. 1 [1 mark]
9. (a) What is an AC source?

(b) I (mA)
60

30

0 0.1 0.2 0.3 t (s)

-30

-60 FIGURE 21.4
FIGURE 21.4 shows a graph of current against time of an AC generator. Determine
the
(i) peak current.
(ii) frequency.
(iii) alternating current equation.

[5 marks]
(c) (i) What is meant by root mean square voltage?

V (V)
(ii) 220

110

0 0.01 0.02 0.03 t (s)

-110

-220 FIGURE 21.5
31

What is root mean square voltage of the AC source in FIGURE 21.5?

[3 marks]
(d) A coil having inductance 0.15 H and resistance 12 Ω is connected across a voltage

source of V = 110 sin (157t). Calculate the

(i) rms current in the coil.
(ii) phase angle between the current and the voltage.

(iii) average power loss in the coil.
[6 marks]

SESSION 2013/2014 DF045/2 No. 1 V
10.
~

LC

R
FIGURE 21.6

FIGURE 21.6 shows an AC source with a maximum voltage of 220 V and frequency 50 Hz
connected to a 70 mH inductor, 40 Ω resistor and 65 μF capacitor.
(a) Write the source voltage equation.

[3 marks]
(b) Calculate the

(i) impedance.
(ii) phase angle.

[8 marks]
(c) Sketch the phasor diagram.

[4 marks]

SESSION 2014/2015 DF045/2 No. 1
11. (a) What is meant by

(i) alternating current (AC)?
(ii) root mean square (rms) current?

[2 marks]

(b)

FIGURE 21.7
32

FIGURE 21.7 shows an AC source, V = 156 sin 120 connected to a 65 mH inductor,
AC ammeter, 10 Ω resistor and a 35 µH capacitor.
(i) Sketch a graph of the AC voltage against time. Label the peak voltage.
(ii) Sketch the phasor diagram of the circuit.
(iii) Calculate the impedance of the circuit.
(iv) Calculate the rms current.
(v) State the quantity measured by the ammeter.
(vi) Is this circuit resonance? Justify your answer.

[13 marks]

ANSWERS:
TOPIC 6: ALTERNATING CURRENT

1. (b) 80 Ω
(a) 220 Ω (b) 266 Ω
(a) 4.83 A (b) 74.7o

2. (a) 300 (b) 43.3 W
(a) (i) 325 V (ii) 0.762 A (iii) 23.9 V (iv) 0.993 (v) 174 W

3. (b) 339.411 V
4. (c) (i) 1.658×103 Ω (ii) 5.1367×105 Hz
5. (b) 80 Ω
6. (b) 7.071A
7. (a) (i) 212.13 V (ii) 1.768 A (iii) 375 W (iv) 212.13 V

(b) (i) 1000 Ω (ii) 25.80 (iii) 0.9
8. (a) (i) 0.34 A (ii) 500 Ω (iv) 57.6 sin 10000 t W, 57.6 W (b) (i) 6.022 Ω (ii) 41.09 Hz
9. (b) (i) 60 mA (ii) 5 Hz (iii) I  60×103 sin10t (c) (ii) 155.6 V

(d) (i) 77.8 A (ii)

TOPIC 7: GEOMETRICAL OPTICS

MAY 2005/2006 SF027/2 No. 1 1.10 m
1.

FIGURE 22.1
A boy 1.20 m tall sees his image in a shining ball hanging from a wall. The ball is 8.50 cm in
diameter and 1.10 m away from the boy as shown in FIGURE 22.1. Calculate his
(a) image distance.

[2 marks]
(b) image height.

[2 marks]

33

SESSION 2006/2007 SF027/2 No. 1
2. An object of height 10 cm is placed 30 cm from a converging lens. The height of the virtual

image formed is 20 cm. Calculate
(a) the image distance.
(b) the focal length of the lens.

[4 marks]

SESSION 2006/2007 SF027/2 No. 9
3. (a) Object

Glass rod

12 cm FIGURE 22.2

An object is placed 12 cm in front of a glass rod with hemispherical tip as shown in

FIGURE 22.2. If the radius of curvature and refractive index of glass is 24 cm and 1.52

respectively,

(i) Calculate the image distance.

(ii) State TWO image characteristics.

[5 marks]

SESSION 2007/2008 SF027/2 No. 1

4. A thin converging lens with refractive index 1.5 has both radii of curvature 20 cm. An object

is placed 10 cm from the lens. Calculate the image distance.

[4 marks]

SESSION 2007/2008 SF027/2 No. 9
5. A concave mirror has a radius of curvature 30 cm. An object height 12 cm forms an enlarged

image 20 cm from the mirror.
(i) Calculate the object distance.
(ii) Calculate the height of the image.
(iii) State the characteristics of the image.

[7 marks]

SESSION 2008/2009 SF027/2 No. 1
6. An object is placed 12 cm in front of a mirror. The real image formed is the same size as the

object.
(a) Determine the focal length of the mirror.
(b) State the type of mirror.

[4 marks]
SESSION 2009/2010 SF027/2 No. 1
7.

FIGURE 22.3
34

FIGURE 22.3 shows a plano-concave lens with index of refraction 1.51 and radius of

curvature 18.0 cm. Calculate focal length of the lens.

[4 marks]

SESSION 2010/2011 SF027/2 No. 9

8. (a) (i) State the laws of reflection.
(ii) State Snell’s law.

[3 marks]

(b) The image formed by a convex mirror is always virtual irrespective of the position of

the object. Verify this statement by using spherical mirror equation.

[3 marks]

(c) A plano-convex lens has refractive index 1.66. The radius of curvature of the convex

surface is 5.28 cm.

(i) Calculate the focal length of the lens.

(ii) If an object of height 0.5 cm is placed 10.0 cm in front of the lens, determine

the size and the characteristics of the image.

[9 marks]

SESSION 2011/2012 SF026/2 No. 6

9. (a) An object 4.0 cm high is placed 15.0 cm from a convex mirror of focal length 5.0 cm.

Determine

(i) The position of the image from the mirror.

(ii) The magnification of the image.

(iii) The height of the image.

[5 marks]

(b) (i) State Snell’s law.

(ii)

FIGURE 22.4

* A laser beam is incident perpendicularly on a prism and leaves the prism
with a deviation angle 200 as shown in FIGURE 22.4. Determine the index of
refraction of the prism. (Index of refraction of air, nair = 1.00)

[5 marks]

SESSION 2012/2013 SF026/2 No. 6 (a) & (b)
10. (a) (i) With the aid of a diagram, explain the Snell’s law of propagation of light from

a dense medium to a less dense medium.
(ii) *The refractive index of diamond is 2.42. Calculate the critical angle of

diamond air interface. Explain the importance of the critical angle in
producing diamond jewellery.

35

[5 marks]
(b) Focal length of a converging biconvex glass lens (n = 1.5) is 20 cm.

(i) Calculate the radius of curvature of the lens.
(ii) If the lens is placed in a liquid of refractive index n = 1.63, calculate the new

focal length and state the lens type.
[5 marks]

SESSION 2012/2013 DF045 No. 2
11. (a) An object is placed 15 cm from a convex mirror with a radius of 10 cm. Draw a

labeled ray diagram to show the formation of the image.
[2 marks]

(b) An object 3 cm high is placed 20 cm from a convex mirror which has a focal length of
8 cm.
(i) Determine the position of the image.
(ii) Determine the magnification of the mirror.
(iii) Determine the height of the image.
(iv) State three characteristics of the image. Justify your answer.
[9 marks]

(c) An object is placed in front of a concave mirror with a 20 cm radius of curvature. A
real image twice the size of the object is formed. At what distance is the object from
the mirror?
[4 marks]

SESSION 2012/2013 DF045 No. 3 [3 marks]
12. (a) (i) State the laws of reflection.

(ii) State Snell’s law.

(b)

35°

air

oil

water

FIGURE 22.5
*A layer of oil (n = 1.45) floats on water (n = 1.33) as shown in FIGURE 22.5. If a
ray of light shines onto the oil with an incident angle of 35º, calculate the angle of
refraction in water.

[3 marks]
(c) A plano-convex lens has refractive index 1.55. The radius of curvature of the convex

surface is 4.25 cm.
(i) Calculate the focal length of the lens.

36

(ii) If an object of height 0.3 cm is placed 12.0 cm in front of the lens, determine
the height of the image.
[9 marks]

SESSION 2013/2014 DF045/2 No. 2
13. (a) State the law of reflection.

[1 marks]
(b) An object is placed 10 cm from a convex mirror of focal length 30 cm.

(i) Calculate the image distance.
(ii) Calculate the magnification of the image.
(iii) State THREE characteristics of the image.

[9 marks]
(c) A real, inverted and diminished image is produced by a spherical mirror. Sketch a ray

diagram showing the formation of the image.
[4 marks]

SESSION 2013/2014 DF045/2 No. 3
14. (a) State Snell’s law.

------------------------------------------- [1 mark]
(b) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

--------------

------------ Glass rod
------------

ob-j-e-c-t- - - - - - - - - -

------------------

- - - - - - - - - - - - - - - - - - - --w-- a-- --te--r-- - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
FIGURE 22.6

FIGURE 22.6 shows a glass rod of refractive index 1.5 immersed in water of

refractive index 1.3. One end of the rod has a spherical surface of radius 20 mm. An

object is placed 80 mm to the left of the rod vertex.

(i) Calculate the image distance.

(ii) Is the image on the left or right side of the rod vertex?

[4 marks]

(c) A biconvex lens of refractive index1.5 has radii of curvature 4 cm and 12 cm.

(i) Calculate the focal length of the lens.

(ii) An object is placed 10 cm to the left of the lens. Calculate the image distance.

(iii) A second lens of focal length 15 cm is placed to the right of the first lens. If

the final image is 25 cm to the left of the second lens, calculate the distance

between the lenses.

[10 marks]

SESSION 2014/2015 DF045/2 No. 2 [2 marks]
15. (a) (i) Define refractive index, n.

(ii) State Snell’s law.

37

(b)

air  a θR R

i

oil ro 5 cm
i
5

Ql Q cα 8 cm
glass g  8

lm c
aP m
sFIGURE 22.7 P

*FIGURE 22.7 shows a lasyer of oil on an 8 cm thick glass slab. The refractive index

of glass is 1.51. A ray originates from point P at the bottom of the glass slab crosses

the glass-oil interface at point Q, 5 cm from vertical line PR. Calculate
(i) the incident angle, α at Q.

(ii) the angle of refraction, θ in air.

[4 marks]

(c)

308 cm

FIGURE 22.8
A thin hemispherical clear plastic bowl of radius 55 cm is placed in a tank filled with
water (n = 1.33). The base of the bowl sinks to a depth of 8 cm and the water level
rises to a height of 308 cm as shown in FIGURE 22.8. An object at the bottom of the
tank is viewed vertically from above the bowl.
(i) Calculate the image distance from the base of the bowl.
(ii) Is the image virtual or real? Justify your answer.

[6 marks]
(d) The radius of curvature of a bi-convex lens is 24 cm. the refractive index of the lens is

1.54. Calculate the focal length of the lens.
[3 marks]

SESSION 2014/2015 DF045/2 No. 3
16. (a) (i) State the law of reflection.

38

(ii) Which mirror can be used to start a fire on a sunny day; convex mirror or

concave mirror? Justify your answer by using ray diagram. How should it be
done?

[5 marks]

(b)
Q (f=15 cm) Q

P (f=5 cm) P

(
O (f

f=
=

8 cm 108cm5 1
15

0
1an0FIocGbmjU.ecRTthEOe 2fcmo2pc.la9acm)cleldeng8thcsmcmofinlefnr)mcsoenst
FIGURE 22.9 shows of two converging lenses,
P and Q separated by P and Q are 5 cm and 15
cm respectively.

(i) Calculate the final image distance from lens Q.

(ii) Calculate the magnification of the final image.

(iii) Determine the three (3) characteristics of the final image.

[10 marks]

ANSWERS:
TOPIC 7: GEOMETRICAL OPTICS

1. (a) -2.08 cm (b) 2.27 cm
2. (a) -60 cm (b) 60 cm
3. (a) (i) – 24.65 cm
4. – 20 cm
5. (a) (i) 8.57 cm (ii) 28 cm
6. (a) 6 cm
7. -35.29 cm
8. (c) (i) 8.0 cm (ii) 2 cm
9. (a) (i) -3.75 cm (ii) 0.25 (iii) 1 cm (b) (ii) 1.28
10. (a) (ii) 24o (b) (i) 20 cm (ii) -125 cm
11. (b) (i) -5.71 m (ii) 0.29 (iii) 0.86 m (c) 15 cm
12. (b) 25.5o (c) (i) 7.73 cm (ii) 0.54 cm

39

TOPIC 8: PHYSICAL OPTICS

SESSION 2005/2006 SF027/2 No. 9 (a)
1. Explain how two coherent light sources can be produced from a single monochromatic light

source based on Huygens’ principle.
[3 marks]

SESSION 2005/2006 SF027/2 No. 9 (b)
2. Monochromatic light from helium-neon laser of wavelength 633 nm is incident normally to a

diffraction grating. If the grating consists of 5000 lines per cm, calculate the angle at which
second order maximum can be observed.

[4 marks]

SESSION 2005/2006 SF027/2 No. 9 (c)
3. (a) Explain why the centre of Newton’s ring is dark.

(b) What is the form of interference pattern if the plano-convex lens is replaced by a
cylindrical lens?
[3 marks]

SESSION 2006/2007 SF027/2 No. 9 (b)
4.

Glass slide air Paper

Glass slide

FIGURE 23.1
*FIGURE 23.1 shows two glass slides separated by thin piece of paper at one end. Explain
with the aid of a diagram, why multi-color fringes can be seen by an observer directly above
the slide.

[5 marks]

SESSION 2006/2007 SF027/2 No. 9 (c)
5. A yellow light of wavelength 589 nm is incident on a diffraction grating with 6000 lines per

cm. calculate the angle of the second bright fringe.
[5 marks]

SESSION 2007/2008 SF027/2 No. 9 (b)

6. State TWO physical differences between interference and diffraction patterns.
[2 marks]

SESSION 2007/2008 SF027/2 No. 9 (c)
7. In a Young’s double slits experiment, the slits are 0.3 mm apart and the distance of the screen

to the slits is 50 cm. The slits are illuminated by an orange light of wavelength 6 x 10-7 m.

(i) Calculate the separation between the adjacent bright fringes
(ii) What will happen to the interference pattern if a light of shorter wavelength is used?

Explain your answer.
(iii) What is observed on the screen if one of the slits is covered? Explain your answer.

40

[6 marks]
SESSION 2008/2009 SF027/2 No. 9 (a)
8. What will happen to light when it passes an obstacle?

[1 mark]
SESSION 2008/2009 SF027/2 No. 9 (b)
9. With the aid of a sketched and labeled diagram, explain the formation of the single slit

diffraction patterns.
[7 marks]

SESSION 2008/2009 SF027/2 No. 9 (c)
10. Light from two sources passes through a 0.5 mm wide slit. A screen is placed 2 m behind the

slit.
(i) What is the condition for a diffraction pattern to be observed on the screen?
(ii) The second bright fringe from a 633 nm light source overlaps with the third dark

fringe from an unknown light source. Calculate the wavelength of the unknown light
source.

[6 marks]

SESSION 2008/2009 SF027/2 No. 9 (d)
11. If the single slit is replaced by a diffraction grating, what will happen to the diffraction

pattern?
[1 mark]

SESSION 2009/2010 SF027/2 No. 9 (a)
12. When viewed at different angles, the colour on compact disc appears to be different, while

the colour of a painted surface appears he same. Explain the difference.
[3 marks]

SESSION 2009/2010 SF027/2 No. 9 (b)
13.

FIGURE 23.2

*FIGURE 23.2 shows a wire separating two pieces of thin glass plates at one end. When a
600 nm light is incident normally, 20 dark bands are observed. Calculate diameter of the
wire.

[4 marks]
SESSION 2009/2010 SF027/2 No. 9 (c)
14. When a 500 nm light is illuminated onto a single slit, a diffraction maximum of width 10 cm

is formed on a screen 2.4 m away from the slit.
(i) Calculate the width of the diffraction maximum if the 500 nm light is replaced by a 650

nm light.

41

(ii) What will happen to the diffraction maximum width if the screen is moved closer to the
slit? Explain your answer.

SESSION 2010/2011 SF027/2 No. 1
15. An oil film floats on water. The refractive indices of the oil and water are 1.30 and 1.33,

respectively.
(a) If the oil film has uniform thickness of 100 nm, calculate the maximum wavelength

of reflected light for destructive interference.
(b) If the colour of the oil film jeeps changing when viewed from the same angle, explain

the reason for the phenomenon.
[4 marks]

SESSION 2011/2012 SF026/2 No. 6 (c)
16. Light 540 nm wavelength is incident on a slit 0.240 mm wide. A screen is placed 2.00 m

from the slit.
(i) Determine the position of the first dark fringe.
(ii) Calculate the width of the central bright.
(iii) What is the effect on the intensity of the central bright fringe if a narrower slit is

used?
[5 marks]

SESSION 2012/2013 SF026/2 No. 6 (c)
17. In a Young’s double-slit experiment, the light source simultaneously emits blue light of

wavelength 400 nm and yellow light of wavelength 600 nm. The slits are 0.08 mm apart and
interference pattern is observed on a screen at a distance of 60.0 cm from the slits. Calculate
(i) The distances of the first blue and the first yellow fringes from the central fringe (that

is, the zeroth fringe).
(ii) The shortest distance from the central fringe where the yellow and blue fringes

overlap.
[5 marks]

SESSION 2012/2013 DF045 No. 4
18. (a) (i) Define coherent light source.

(ii) State the conditions for constructive and destructive interferences.

(b) Coherent light with a wavelength of 475 nm is incident on a double slit and its
interference pattern is observed on a screen at 85 cm from the slits. The third bright
fringe occurs at 3.11 from the central maximum. Calculate
(i) Separation distance between slits
(ii) Distance from the central maximum to the third dark fringe.

(c) (i) Sketch ray diagram to show the formation of the interference in air wedge.
(ii) *Two thin glass plates 20 cm long are in contact at one end and separated by a
40 μm thick foil at other end. Determine the separation of the interference
fringes when the plates are illuminated by alight of wavelength 546 nm.
[15 marks]

42

SESSION 2012/2013 DF045 No. 5
19. (a) (i) Define diffraction.

(ii) State two factors that determine the intensity of diffraction patterns.
(b) A slit is illuminated with light of wavelength 650 nm and the first minimum

appears at 10°.
(i) Calculate the width of the slit
(ii) The slit is illuminated with a light of different wavelength and the first

maximum appears at the same angle. Calculate the wavelength of the light
used.
(c) (i) Explain briefly the formation of the diffraction patterns by a diffraction
grating.
(ii) A diffraction grating having 7000 lines per cm is illuminated with red light.
The second order maximum is at 62°. Calculate the wavelength of the red
light.

[15 marks]
SESSION 2013/2014 DF045/2 No. 4
20. (a) (i) State Huygen’s principle.

(ii) State TWO conditions for the observation of the interference of light.
(iii) Use Huygen’s principle to explain the diffraction of light from a single slit.

[6 marks]
(b) A plate with double-slits is illuminated by a 550 nm light and produces fringes on a

screen 1.3 m from the plate.
(i) If the separation of the slits is 0.2 mm, calculate the separation between two

consecutive dark fringes.
(ii) If the double-slits plate is replaced with a single-slit plate of width 9 μm,

calculate the approximate width of the central bright fringe.
(iii) The plate is replaced with a diffaction grating with 2.4×105 lines per meter.

Calculate the angle of the second order diffraction.
[9 marks]

SESSION 2013/2014 DF045/2 No. 5
21. (a)

Spherical surface glass

Flat glass plate

FIGURE 23.3

*FIGURE 23.3 shows an air wedge formed between a spherical glass surface and a
flat glass plate.
(i) Sketch the interference pattern when viewed at normal incidence.
(ii) Sketch and explain the formation of the interference pattern.

[9 marks]
(b) A thin soap film of refractive index 1.35 on top of a flat glass plate of refractive index

1.50 is illuminated by a 600 nm red light. When viewed at normal incidence,
calculate the

43

(i) minimum film thickness if it appears red.

(ii) minimum film thickness for it to be dark.

[6 marks]

SESSION 2014/2015 DF045/2 No. 4
22. (a) (i) State Huygens’ principle.

(ii) What is meant by coherent light sources?

[3 marks]

(b) (i) State the conditions for the destructive and constructive interferences.

(ii) Interference pattern of a double-slit is observed on a screen at a distance 1.5 m

away. The slits are 0.25 mm apart and illuminated by a light of a wavelength

589 nm. Calculate the saperation between adjacent bright fringes.

[4 marks]

(c) *Two glass plate form an air wedge. Light of wavelength 589 nm is illuminated on

the plates and 6 dark fringes are seen. What is the maximum thickness of the air

wedge?

[3 marks]

(d) *Use a diagram to explain the formation of Newton’s rings.

[5 marks]

SESSION 2014/2015 DF045/2 No. 5

23. (a) State the differences between the diffraction and interference patterns in terms of
intensity and width of the fringes.

[2 marks]

(b) l
light i

g

h

tair a
Pi
P Qr

FIGURE 23.4

*FIGURE 23.4 shows an air wedge between two glass plates. The separation
between the plates at Q is 45 µm. The air wedge is illuminated at normal incidence by
a 552 nm light.
(i) Explain the formation of interference fringes in the air wedge with the aid of

diagram.
(ii) Calculate the number of dark fringes that could be observed.
(iii) If light with larger wavelength is used, what will happen to the separation of

the fringes; closer, stay the same or further apart? Explain your answer.
[9 marks]

44

(c)

incident ray I

n

c

n1=1.38 i n t t

d 1

n2=1.50 e n

FIGtnURE=2 23.5 of
Artreafnrtasrcpatnaivsreepnatrineldnateyxelraynae2srs=hoofw1r.n5ef0irn.acFAtriIvGerUeidnR=.1dEelixgh2t3n.15of=buwt1an.v3oe8lreencfgloetvcheter6ds 8a0lightnrtmanissipsoabrisenencrtidveemdnet. doiunm the

(i) Why does such phenomaenon 13occur?
(ii) Calculate the minimum ythick8.ness of the transparent layer, t.

5 [4 marks]

ANSWERS: 0

TOPIC 8: PHYSICAL OPTICS

2. 2×10-6 m

5. 44.98°
7. (i) 1×10-3 m

10. (ii) 527.5 nm
13. 5.7×10-6 m

14. (i) 0.13 m
15. (a) 5.2×10-7 m
16. (i) 4.5×10-3 m (ii) 9×10-3 m
17. (i) 3×10-3 m, 4.5×10-3 m (ii) 9×10-3 m
18. (b) (i) 1.3×10-5 m (ii) 3.24×10-5 m (c) (ii) 1.56×10-5 m
19. (b) (i) 3.7×10-6 m (ii) 6.42×10-7 m (c) (ii) 6.31×10-3 m

TOPIC 9: QUANTIZATION OF LIGHT

SESSION 2005/2006 SF027/2 No. 6
1. (a) State ONE characteristic of electromagnetic wave energy that contradicts between the

Planck’s theory and classical theory.
[1 mark]

(b) Ultraviolet waves with frequency from 8.00 × 1015 Hz to 1.00 × 1017 Hz are incident
on a zinc surface. The work function of zinc is 4.33 eV. Calculate the maximum
kinetic energy of electrons ejected from the surface.
[3 marks]

SESSION 2008/2009 SF027/2 No. 13
2. (a) State two important observation from the photoelectric experiment that support the

Planck’s Quantum Theory. Explain each of your answer.

45

[2 marks]

(b)

Light F
source

Ammeter

Evacuated CC A
glass chamber T T

V

FIGURE 24.1

FIGURE 24.1 shows the schematic set-up of a photoelectric effect experiment. Light

with intensity I0 is illuminated towards an evacuated glass chamber that chamber that
housed the target T and plate C.

(i) Why current is detected by ammeter although the set-up appears to be an

incomplete circuit?
(ii) State three critical steps in the experiment that enable the determination of the

stopping potential. Explain your answer.

(iii) Sketch on the same axes labeled graphs of the current, I against the voltage, V

for light intensities, I0 and ½ I0. Label the stopping potential.

[10 marks]

SESSION 2009/2010 SF027/2 No. 13
3. (a) State the differences and similarity between an electron and a photon.

[3 marks]
(b) In a photoelectric experiment, no photoelectron is emitted even though light is

illuminated on the target metal. Will the photoelectrons be ejected from the metal by
increasing the intensity of the light source? Explain your answer.

[2 marks]

SESSION 2010/2011 SF027/2 No. 13 (a)
4. (a)

46
FIGURE 24.2

FIGURE 24.2 shows the setup of a photoelectric experiment. Several filters of different
colours of known wavelength are provided.
(i) State the function of the colour filters, voltmeter and microammeter.
(ii) Where should the material under test be placed?
(iii) What are the parameters to be measured so that the work function of the test material

could be determined?
(iv) How to determine the Plank’s constant?
(v) What is the implication of this experiment?

[8 marks]

SESSION 2011/2012 SF026/2 No. 7 (a)
5. A cesium surface is illuminated with light of wavelength 380 nm. The work function for

cesium is 2.14 eV. Calculate
(i) The energy of the photon in eV.
(ii) The maximum kinetic energy of the photoelectrons.
(iii) The threshold frequency for cesium.
(iv) The stopping potential for the photoelectrons.

[10 marks]

SESSION 2012/2013 SF026/2 No. 7
6. (a) Explain the following terms:

(i) Photon.
(ii) Work function.
(iii) Photoelectric current.

[4 marks]
(b) The minimum frequency of the electromagnetic radiation which will cause

photoelectric emissions from a metal is 4.70 1014 Hz.
(i) Calculate the work function of the metal in eV
(ii) If the metal surface is hit by electromagnetic radiation of frequency

7.1x1014 Hz, calculate the maximum kinetic energy of the photoelectron.
[5 marks]

SESSION 2012/2013 DF045 No. 6
7. (a) (i) Explain photoelectric effect.

(ii) State two classical theory assumptions that contribute to its failure to explain
the photoelectric effect.

(b) In a photoelectric effect experiment, a beam of light of wavelength 400 nm is incident
on a sodium surface. The work function of sodium is 2.28 eV. Calculate
(i) threshold wavelength of sodium
(ii) maximum kinetic energy of the photoelectrons
(iii) stopping potential of the photoelectrons
(iv) maximum velocity of ejected photoelectrons

(c) (i) State wave particle duality of matter.
(ii) Calculate the de Broglie wavelength for an electron moving at 3.25 x 105 ms-1.

47

[15 marks]

SESSION 2013/2014 DF045/2 No. 6 (a) (i) & (b)
8. (a) What is meant by work function?

[1 mark]
(b) A photocell detects light by means of the photoelectric effect. You are given a cesium

photocell with work function 2.1 eV and an aluminum photocell with work function
4.3 eV.
(i) What is the threshold frequency of the cesium and aluminum photocells?
(ii) Which of the photocells will you use to detect visible light in the range of 400

nm to 700 nm? Explain your answer.
(iii) Calculate the maximum speed of the emitted electron in the cesium photocell

if a 250 nm light is shone on it.
[12 marks]

SESSION 2014/2015 DF045/2 No. 6 (b)
9. An ultraviolet ray of wavelength 124 nm strikes a metal surface and electrons are ejected

spontaneously from the surface. The maximum kinetic energy of the ejected electron is 4.16
eV.
(i) Why did the classical theory of the energy fail to explain the spontaneous emission of

the electron?
(ii) State the stopping potential for the ejected electrons.
(iii) Calculate the threshold frequency.
(iv) If the intensity of light is increased, will the maximum kinetic energy of the ejected

electron decrease, remain unchanged or increase? Explain your answer.
(v) If the frequency of light is increased, will the observed threshold frequency decrease,

remain unchanged or increase? Explain your answer.
[12 marks]

ANSWERS:
TOPIC 9: QUANTIZATION OF LIGHT

1. (b) 410 eV
5. (i) 3.27 eV (ii) 1.13 eV (iii) 5.16x1014 Hz (iv) 1.13 V
6. (b) (i) 1.948 eV (ii) 1.59×10-19 J or 0.995 eV
7. (b) (i) 5.45×10-7 m (ii) 4.97×10-4 J (iii) 3.11×1015 V (iv) 7.72×1011 J

(c) (ii) 2.24×10-9 m

TOPIC 10: WAVE PROPERTIES OF PARTICLE

SESSION 2006/2007 SF027/2 No. 6

1. Calculate the de Broglie wavelength of an electron that is accelerated through a potential
difference of 700 V.
[3 marks]

48

SESSSION 2007/2008 SF027/2 No. 13 (a)

2. Why do moving electrons be diffracted by a single crystal? [3 marks]
SESSION 2008/2009 SF027/2 No. 6 (a)

3. The wavelength  of a particle Q with momentum p is related by the equation   h .
p

(a) What do  and p represent with respect to the nature of the particle Q?
(b) What happens to  when the particle Q is at rest?

[3 marks]
SESSION 2009/2010 SF027/2 No. 13 (a), (c) & (d)

4. (a) State the differences and similarity between an electron and a photon.
[3 marks]

(b) Why does an electron microscope need high velocity electrons?
[2 marks]

(c) A particle has a de Broglie wavelength . Calculate the new de Broglie wavelength of
the particle in terms of  if
(i) The kinetic energy is quadrupled.
(ii) The momentum is quadrupled.
[5 marks]

SESSION 2011/2012 SF026/2 No. 7 (b) & (c)

5. (a) Name one experiment that verifies the wave nature of electrons. [1 mark]
[4 marks]
(b) An electron has a de Broglie wavelength   2.01011 m. Calculate
(i) The momentum of the electron.
(ii) The speed of the electron.

SESSION 2012/2013 SF026/2 No. 7

6. (i) State de Broglie hypothesis.
(ii) In an experiment, electrons are accelerated from rest through a potential difference of
3 MV. Determine de Broglie wavelength, the momentum and kinetic energy of the
electrons.
[6 marks]

SESSION 2013/2014 DF045/2 No. 6 (a) (ii)

7. State ONE advantage of electron microscope compared to light microscope. Explain your
answer.
[1 mark]

SESSION 2014/2015 DF045/2 No. 6 (a)

8. (i) State the wave-particle duality.
49