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CHAPTER 4

MAGNETISM

LEARNING OUTCOMES
At the end of this chapter, students should be able to :

4.1 Magnetic field
a) Define magnetic field.
b) Identify magnetic field sources.
* Example:
i. Bar magnet and current-carrying conductor (straight wire, circular coil, and
solenoid).
ii. Earth magnetic field.
c) Sketch magnetic field lines for
i. Bar magnet and current-carrying conductor (straight wire, circular coil, and
solenoid).
ii. Earth magnetic field.

4.2 Magnetic field produced by current-carrying conductor
a) Sketch resultant magnetic field diagram at a point (limited to two current carrying
straight wires and 2D).
b) Determine direction of ⃑ by using right hand rule.
c) Determine the magnitude of magnetic field by using:
i) B   0 I for a long straight wire
2r
ii) B   0 I at the centre of a circular coil
2r

iii) B  0 nI at a centre of a solenoid
iv) B  0 nI at the end of the solenoid

2
4.3 Force on a moving charged particle in a uniform magnetic field

a) Use magnetic force, F  qv  B
b) Determine direction of force.
c) Describe circular motion of a charge in a uniform magnetic field.
c) Use relationship FB = Fc.
4.4 Force on a current-carrying conductor in a uniform magnetic field
a) Use magnetic force = × ⃑
b) Determine direction of force.
4.5 Forces between two parallel current-carrying conductors
a) Explain magnetic force per unit length of two parallel current-carrying conductors.
b) Use magnetic force per unit length, F  o I1I2

l 2 d

4.6 Torque on a coil

a) Use torque,   N I A B where N = number of turns.

b) Explain briefly the working principles of a moving coil galvanometer.

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4.7 Application of motion of charged particle
a) Explain the motion of a moving charged particle in magnetic field and electric field
for v, B and E perpendicular to each other.
b) use velocity, v =E/B in a velocity selector. (e.g. Brainbridge mass spectrometer)

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4.1 Magnetic Field

1. A bar magnet is divided in two pieces. Which of the following statements is true?
A. The bar magnet is demagnetized.
B. The magnetic field of each separated piece becomes stronger.
C. The magnetic poles are separated.
D. Two new bar magnets are created.

1.
2. Which of the following magnetic fields is correct for a single bar magnet?

A.

B.

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C.
D.

3. A current-carrying wire is placed perpendicular to the page. Determine the direction of the
electric current from the direction of the magnetic field as shown below.

A. Into the page.
B. Out of the page.
C. Clockwise.
D. Counter-clockwise.

4. Sketch magnetic field lines for

a) Straight wire.
b) Solenoid.

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4.2 Magnetic Field Produced by Current-carrying Conductor

5. A vertical wire carries an electric current into the page as shown below. What is the direction
of the magnetic field at point P located to the south from the wire?

A. West.
B. North.
C. East.
D. South.

6. A vertical wire carries an electric current out of the page as shown below. What is the
direction of the magnetic field at point P located to the west from the wire?

A. West.
B. North.
C. Down.
D. South.

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Figure 1
7. Two parallel long straight rigid wires X and Y carry the same current of 20 A in opposite

directions as shown in the Figure 1. The wires are 10 mm apart. Point P is 5.0 mm from wire
X. Determine the resultant magnetic field at point P.

8. Calculate the value of the magnetic flux density, B in an air-core solenoid that has
2000 turns m-1 length when the current in the solenoid is 0.10 A .

4.3 Force on a Moving Charged Particle in a Uniform Magnetic Field

9. An electron moves into a uniform magnetic field with a certain velocity. If the velocity of the
electron is in the same direction as the magnetic field, which statement about the subsequent
motion of the electron in the magnetic field is true?
A. The electron accelerates to the left.
B. The electron accelerates to the right.
C. The electron continues to move with its original velocity.
D. The electron is deflected and moves in a circle at constant speed.

10. A positive charge moving with a constant velocity v enters a region of a uniform magnetic
field pointing out of the page as shown below. What is the direction of the magnetic force on
the charge?

A. Left.
B. Right.
C. To the bottom of the page.
D. To the top of the page

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11. A negative charge moving with a constant velocity v enters a region of a uniform magnetic
field pointing out of the page as shown below. What is the direction of the magnetic force on
the charge?

A. Left.
B. Right.
C. To the bottom of the page.
D. To the top of the page
12. An electron enters a region of a uniform magnetic field of magnitude 1.00 mT which pointing
into the page. Determine the speed of the electron in terms of r.

13. A proton travels with a speed of 3.00 × 106 m s-1 at an angle of 37.0° with the
direction of a magnetic field of 0.300 T in the +y direction. What are the magnitude of
the magnetic force on the proton and its acceleration? Sketch the path of proton if its
magnetic force is maximum.

4.4 Force on a Current-carrying Conductor in a Uniform Magnetic Field
14. A straight long wire carries an electric current to the right. The current is placed in a uniform

magnetic field directed into the page as shown below. What is the direction of the magnetic
force on the current?

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A. Left.
B. Right.
C. To the bottom of the page.
D. To the top of the page

15. A copper wire of length 12.0 cm is placed at an angle 50° to the vertical. A uniform
magnetic field of strength 0.2 T is oriented to the horizontal. If the wire carries a
current of 5 A, calculate the magnetic force on this wire.

16. A conductor suspended by two flexible wires as shown in Figure 2 has a mass per
unit length of 0.0400 kg m-1. What current must exist in the conductor in order for the
tension in the supporting wires to be zero when the magnetic field is 3.6 T into the
page? What is the required direction for the current?

F

Bin

Figure 2

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4.5 Forces between Two Parallel Current-carrying Conductors

17. Two long, straight parallel wires X and Y are separated by a distance d. The force between
the wires is F when the current in both the wire is I. The current in both the wires is increased
to 2I, what is the separation between the wires so that the force between the wires remains as
F?
A. d/4
B. d/2
C. 2d
D. 4d

18. Two long, parallel vertical wires separated by a distance of 0.3 m, are placed east-west of one
another. The current in the westerly wire is 20 A and the other is 30 A. Both currents flow
upwards. If the horizontal component of the Earth’s magnetic flux density is 2.0 x 10-5 T,
calculate the resultant force on one metre length of each wire.

4.6 Torque on a Coil

19. Moving Coil Galvanometer uses phosphor-bronze wire for suspension because it has
A. High Conductivity
B. High Sensitivity
C. A large couple per unit twist
D. Small couple per unit twist

20. The working principle of a moving coil galvanometer is
A. magnetic field
B. current
C. electric field
D. torque

21. A current of 17.0 mA is maintained in a single circular loop of 2.00 m circumference.
A magnetic field of 0.800 T is directed parallel to the plane of the loop. What is the
magnitude of the torque exerted by the magnetic field on the loop?

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22. A galvanometer needle deflects full scale for a 53.0-A current. What current will give full-
scale deflection if the magnetic field weakens to 0.860 of its original value?

4.7 Application of Motion of Charged Particle
23. What is the path of electric charged move in magnetic field and electric field that

perpendicular to each other?
A. circle
B. curved downward
C. curved upward
D. straight line
24. A magnet brought near an old-fashioned TV screen (TV sets with cathode ray tubes instead of
LCD screens) severely distorts its picture by altering the path of the electrons that make its
phosphor glow. To illustrate this, calculate the radius of curvature of the path of an electron
having a velocity of 6.00 × 107 −1(corresponding to the accelerating voltage about 10.0
kV used in some TVs) perpendicular to the magnetic field of strength B=0.005 T(obtainable
with permanent magnets).
25. Protons move in a circle of radius 5.10 cm in a 0.566 T magnetic field. What value of electric
field could make their paths straight? In what direction must it point?

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PB/PTP

PENGAKUAN TUGASAN PELAJAR

PROGRAM MATRIKULASI KEMENTERIAN PENDIDIKAN MALAYSIA
STUDENT’S DECLARATION

MINISTRY OF EDUCATION MALAYSIA MATRICULATION PROGRAMME

Pengakuan Pelajar/ Student’s Declaration

Nama Pelajar / Student’s Name: Kursus / Course: Fizik / Physics No. Matrik / Matric No.:
Kod / Code: EP 025

Tajuk Tugasan: Assignment Topic 4 : Magnetism

Saya mengaku bahawa tugasan ini adalah hasil kerja saya sendiri kecuali nukilan dan ringkasan yang setiap satunya
saya jelaskan sumbernya.

I declare that this task is my own work except for the citations and summaries of which I acknowledged the source.

Tandatangan/ Signature: _________________________ Tarikh/ Date: ____________
()

Nota: Borang ini hendaklah dikepilkan bersama tugasan bertulis/ bercetak/ model dan diserahkan kepada
pensyarah yang memeriksa tugasan.

71

TUTORIAL CLASS PHYSICS UNIT
STUDENT’S NAME KOLEJ MATRIKULASI KEJURUTERAAN KEDAH

TUGASAN BERTULIS / WRITTEN ASSIGNMENT EP 025
TOPIC 4 : MAGNETISM

: ___________________________________________
: ___________________________________________

SUBATTRIBUTE 1 2 3 4 EXAMINER MODERATOR
/20 /20
1. Problem Not able to Able to explain Able to explain Able to provide
Identification the problems explanation of
explain the the problems with 2 problems very
2. Analysis concepts. clearly and
problems with 1 concept. accurately with
3. Relevance of more than 2
References concepts.

4. Originality Find difficulty Able to Able to Able to
and creativity in organising
and analysing organise and organise and organise and
5. Creativity and gathered
neat information or analyse analyse analyse
data and find
difficulty in gathered gathered gathered
describing the
root of the information or information or information or
problem.
data, but does data and data and

not clearly almost clearly clearly

describe the describe the describe the

root of the root of the root of the

problem. problem. problem.

No relevant One relevant Two relevant More than two
reference reference references relevant
given. given given references
according to according to given
APA citation APA citation according to
format format APA citation
format
Perform a task Perform a task Perform a task Perform a task
with lack of with limited with with trust,
trust, honesty, trust, honesty, acceptable honesty,
sincerity and sincerity and trust, honesty, sincerity and
transparency. transparency. sincerity and transparent in
transparency. most
situations.
No creativity at Show creativity
all. in presentation Show creativity

Didn’t answers Answers most in Give ‘wow’

all questions questions presentation. impact.

corretly. correctly. All answers All answers
correctly given correctly given
but missing with unit and
some units and diagram (if
minor error in necessary)
diagram (if
necessary)

TOTAL

EXAMINER’S SIGNATURE, MODERATOR’S SIGNATURE,
………………………………….
……………………………… ()
()
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CHAPTER 5: ELECTROMAGNETIC B : magnetic field strength
INDUCTION A : area of the coil
θ : angle between B and normal

of area A
N : numbers of turns for the coil

Example 5.1

SUBTOPIC  6.0(3104 ) cos 60
5.1 Magnetic Flux
5.2 Induce emf   B A cos
5.3 Self Inductance
5.4 Energy stored in inductor  0.9103 T m2
5.5 Mutual Inductance
5.6 Back emf in DC motor Flux linkage is the magnetic flux
running through, or "linked" to a coil,
A current carrying conductor so the field strength times the coil
produce magnetic field surrounding area. Flux linkage is the magnetic
the conductor. flux running through, or "linked" to a
coil, so the field strength times the coil
Can magnetic field create flow of
current? A magnetic field going through a coil of
Yes, this phenomenon call wire has a property known as flux
Electromagnetic Induction linkage. This is the product of the flux
Φ and the number of coils in the wire
If the coil is composed of N turns, all of N
the same area A, thus the magnetic
flux through N turns coil (magnetic flux Φ =Nø
linkage ) is

where

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5.2 (a) Electromagnetic Induction Moving the magnet away from the
Electromagnetic induction is the loop decreases the number of
production of induced e.m.f.s or magnetic field lines passing
induced currents whenever the through the loop. The induced
magnetic flux through a loop, coil or current is now in opposite direction.
circuit is changed.
Consider the experiment below From the experiments, it can seen
that e.m.f is induced only when the
When there is no relative motion magnetic flux through the coil
between the magnet & the loop, G change.
shows no deflection. No induced
current No change in magnetic flux,
electromagnetic induction cannot
Moving the magnet toward the loop occur.
increases the number of field lines It was further shown that induced e.m.f
passing through loop. The G needle increase when:
is deflected indicating an induced
current is produced (a) a stronger magnet is used,
i.e, magnetic flux is
increased

(b) the magnet is pushed faster
into the coil, i.e the speed of
magnet is increased

(c) the area of the coil is greater.
(d) the number of turns

increased.

5.2 (b) Faraday’s Law of Induction
The induced e.m.f. in a closed loop
depends on the time rate of change of
the magnetic flux through the loop
express mathematically:

   d NBA cos
dt

* minus sign (–) give an indication

of the direction of the induced
e.m.f. ( Lenz’s law )

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5.2 (c) State and use Len’z Law Solution
the direction of induced e.m.f. / current As the magnet moves to the right, the
is always in such a direction that is magnetic flux through the loop
opposes the change in the magnetic increases.
flux that causes it.
By Lenz’s law, the induced current
The induced current produced a north must flow in such a direction that
pole to oppose the incoming north producing a magnetic field directed to
pole. the left of the coil. This oppose the
change of the original magnetic flux.

SN

The induced current is
anticlockwise ; point A is + ; point B
is – .

Induced e.m.f in a plane coil
(1) Changing area in magnetic
field

EXAMPLE Stretching the coil reduces the area,
Figure shows a permanent magnet
approaching a loop of wire. The changes the flux and therefore an
external circuit attached to the loop
consists of the resistance R. Find the induced emf & current are
direction of the induced current and
the polarity of the induced emf geFnroemra:teΦd.= NBA cos θ
As the area A change, flux
change
A↓ Φ↓
Flux change  Induced emf /
current

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According to Faraday’s Law EXAMPLE
The flexible loop has a radius of 12 cm
   d   d (BA cos ) and is in a magnetic field of strength
0.15 T. The loop is grasped at point A
dt dt and B and stretched until its area is
nearly zero. If it takes 0.20 s to close
( * B is perpendicular to the plane the loop, find the magnitude of the
of coil θ=0° ; cos 0 = 1 & average induced emf in it during this
magnitude of B remain constant) time.

   B dA × ×A× × ×

dt × ××××

(2) Changing magnetic field × ××××
strength. B
× × B×

From: Φ = NBA cos θ EXAMPLE
As the B change, flux change
A circular coil has 200 turns and
B↓ Φ↓ diameter 36 cm. the resistance of the
Flux change  Induced emf / coil is 2.0 Ω. A uniform magnetic field
current is applied perpendicularly to the plane
According to Faraday’s Law of the coil. If the field changes
uniformly from 0.5 T to 0 T in 0.8s.
   d   d (BAcos )
dt dt

( * B is perpendicular to the plane
of coil & A constant)

   A dB

dt

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××

a) Find the induced e.m.f. & e.m.f. induced in a straight
current in the coil while the field conductor moving through a
is changed. magnetic field.

(b) Determine the direction of
the current induced.

Solution
Given :
N = 200 ,
d = 36 × 10-2 m,
R = 2.0 Ω
B change from 0.5 T  0 T in 0.8 s

When the metal rod ( conductor )
moves at a constant speed (v) , a
current is induced in the rod as a result
of the changing flux.
The magnetic field, B is constant
The changing of flux is due to the
change in the area of the circuit, A as
the rod is moved to left.
According to Faraday’s Law

   d

dt
  d (BAcos )

dt

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Knowing that B is constant and the Direction of induced current flowing
angle between normal of plane with thought the conductor can be
B is 0° , thus we have: determined using Right Hand Rule.

   B dA (1) Another Alternative
dt
The magnitude of the e.m.f. induced
As the rod is pulled, the area of the is
circuit increases by an amount
  Blv sin
dA  l dx
Direction of current induced apply
At constant speed, the distance Fleming Right Hand rule
traveled by the rod in a time interval

dt isdx  v dt

Thus we have :

dA  l vdt

dA  l v (2)
dt

Substitute (2) into (1):

In general form :
The magnitude of the e.m.f. induced
is

  Blv sin

where
B : magnetic field strength
l : length of the conductor
v : velocity of conductor
θ : angle between B and v

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EXAMPLE e.m.f. induced in a Rotating Coil
Consider the arrangement shown in
figure.

Assume that R = 6 Ω, L = 1.2m & a From: Φ = NBA cos θ /
uniform 2.50 T magnetic field is As the θ change, flux change
directed into the page. (a) At what
speed should the bar be moved to θ↓ Φ↓
produced a current of 0.5A in the Flux change  Induced emf
resistor. (b) what is the direction of
the induced current ? current

Solution As a coil rotates in a uniform
magnetic field, the magnetic flux
through the area enclosed by the
coil changes with time; this induces
an e.m.f. & a current in the coil
according to Faraday’s Law.

Suppose that, coil has N turns, all of

the same area A & rotates in a

magnetic field with a constant
angular velocity ω.

(b) Applying Right Hand Rule,
the direction of the induced current
is from b  a  d  c  b
( anticlockwise )

θ : angle between Normal A and B

The induced e.m.f. in the coil :

   d

dt
   d (NBA cos )

dt

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Knowing that values of B, N and A 5.3 Self inductance
are constant and only the LEARNING OUTCOMES
orientation of the coil, θ changes
with time a) Define self-inductance.
b) Apply self-inductance, L = -
Example 5.6
/(dI/dt) for a coil and
solenoid.

5.3 (a) Self Inductance
Self Induction is a phenomenon
where any circuit that carries a varying
current will have an emf induced in it
by the variation in its own magnetic
field.

A loop of area 0.10 m2 is rotating at When the switch is closed, the
60 rev/s with its axis of rotation current produces its own magnetic
perpendicular to a 0.20 T magnetic flux through the circuit.
field. (a) If there are 1000 turns on
the loop, what is the maximum As the current increases from 0 to
voltage induced in the loop? (b) its maximum value with time, the
When the maximum induced magnetic flux through the circuit
voltage occurs, what is the due to this current also increase
orientation of the loop with respect with time.
to the magnetic field?
As the flux is changing, for
opposing the increasing of this
magnetic flux, an induced emf /
current is produced in the circuit
and the direction of the induced
current is opposed the direction of
the current produced by the battery.

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Induced current is indicated by the L depends on the geometry of the
dashed arrow. circuit & other physical characteristics
5.3 (b) Apply Self-Inductance
This effect is called self induction Self Inductance of a coil:
because the changing flux through
the circuit & the induced emf arise
from the circuit itself.

The emf set up is called self where
induced emf / back emf. L : self inductance
N : number of turns
Self induced emf is always Φ : magnetic flux in the coil
proportional to the time rate of I : current flowing in the coil
change of the source current.
Self Inductance of a solenoid

Self Inductance, L is the ratio of the or
self induced emf to the rate of
change of current in the conductor. where L : self inductance

where N : number of turns

is the induced emf μo : permeability of free space
dI/dt is the rate of change of source ( 4π × 10–7 T m A–1 )
current
L is a proportionality constant called A : cross sectional area of the
Self Inductance.
SI unit for L : Henry ( H ) or V s A-1 or solenoid
Wb A-1
l : length of the solenoid

n : number of turns per unit length

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5.4 Energy stored inside inductor
LEARNING OUTCOME

a) Use energy stored inside
inductor as

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CHAPTER 5

ELECTROMAGNETIC INDUCTION

LEARNING OUTCOMES
At the end of this chapter, students should be able to:

5.1 Magnetic flux
a) Define and used magnetic flux,
b) Use magnetic flux linkage, Φ =Nø

5.2 Induced emf
a) Use Faraday’s experiment to explain induced emf by using Faraday’s experiment

b) State Faraday’s law and use Faraday’s law,    d
dt

c) State and use Lenz’s law to determine the direction of induced current.
d) Derived and use induced emf:

i. in straight conductor,  Blvsin

ii. in a coil   NA d ,   NB dA
dt dt

iii. in rotating coil ,  NAB sin t

5.3 Self-inductance
a) Define self-inductance.
b) Apply self-inductance, L    for coil
dI / dt
and solenoid where ;

i. L = N
I

ii L coil = o N 2 A
2r

iii. L solenoid = o N 2 A
l

5.4 Energy stored in an inductor

a) Use the energy stored in an inductor , U  1 L I 2
2

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5.5 Mutual Inductance
a) Define mutual inductance.

b) Use mutual inductance , M  0 N1N2 A


between two coaxial solenoids
5.6 Back emf in DC motor

a) Explain back emf and its effect on DC motor.

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1. An airplane with a wing span of 30.0 m flies parallel to Earth’s surface at a location at
which the downward component of Earth’s magnetic field is 0.6 x 10-4 T. Find the difference in
potential between the wing tips when the speed of the plane is 250 ms-1.
A. 0.45 V
B. 0.35 V
C. 0.65 V
D. 0.25 V

2. If the resistance in the circuit is 0.50 ohm and emf is 0.25 V, find the current in the circuit and the
amount of energy delivered to the 0.50 ohm resistor in 1 s.
A. 0.7 A, 0.11 J
B. 0.5 A, 0.13 J
C. 0.6 A, 0.14 J
D. 0.8 A, 0.15 J

3. Faraday’s Law states that the induced emf is directly propotional to the different rate of
A. magnetic field
B. electric field
C. magnetic flux
D. electric flux

4. The energy stored in an inductor is in
A. the electric field
B. the magnetic field
C. the form of heat
D the form of kinetic energy

5.1 Magnetic flux

5. (a) What is the difference between magnetic flux,Φ and magnetic flux density (magnetic
field), B ?

(b) A small surface area 10 mm2 inside a uniform magnetic field of strength 0.50 T is
inclined at an angle of to the direction of the field. Determine the magnetic flux through
the surface if
i. θ= 0o
ii. θ= 30o
iii. θ= 90o

5.2 Induced emf

6 (a) The plane of a rectangular coil, 5.0 cm by 8.0 cm, is perpendicular to the direction of a
magnetic field B. If the coil has 75 turns and a total resistance of 8.0 Ω, at what rate must the
magnitude of B change to induce a current of 0.10 A in the winding of the coil?

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(b) A circular coil of radius 20 cm is placed in an external magnetic field of strength 0.2 T so that
the plane of the coil is perpendicular to the field. The coil is pulled out of the field in 0.30 s.
Find the average induced emf during this interval.

(c) A 25 turn circular coil of wire has a diameter of 1.0 m. It is placed with its axis along the
direction of earth’s magnetic field of 50.0 μT, and then in 0.20 s it is flipped 180°. An
average emf of what magnitude is generated in the coil?

(d) The plane of a rectangular coil, 5.0 cm by 8.0 cm, is perpendicular to the direction of
a magnetic field B. If the coil has 75 turns and a total resistance of 8.0 Ω, at what
rate must the magnitude of B change to induce a current of 0.10 A in the winding of
the coil?

7. (a) A 50-turn rectangular coil of dimensions 5.00 cm × 10.0 cm is allowed to fall from a
position where B=0T to a new position where B = 0.500T and is the magnetic field directed
perpendicular to the plane of the coil. Calculate the magnitude of the average emf that is
induced in the coil if the displacement occurs in 0.250s.

(b) A flat loop of wire consisting of a single turn of cross-sectional area 8.00 cm2 is
perpendicular to a magnetic field that increases uniformly in magnitude from 0.500 T to
2.50 T in 1.00 s. What is the resulting induced current if the loop has a resistance of 2.00 Ω?

8. (a) A rod of length 4 m is held horizontal with its axis in an east-west direction. It is allowed. To
fall straight down. The speed of the rod is 2.5 ms-¹ and the earth’s magnetic field is 0.5 G. At
an angle 60º below the horizontal. Determine:

i. the induced emf in the rod,
ii. the magnetic force on the rod if the total resistance of the rod is 3Ω and the power

delivered by the magnetic force.

(b) A coil of area 0.100 m2 is rotating at 60.0 rev s-1 with the axis of rotation perpendicular to a
0.200 T magnetic field.
i. If the coil has 1000 turns, what is the maximum emf generated in it?
ii. What is the orientation of the coil with respect to the magnetic field when the
maximum induced voltage occurs?

9. a) An AC generator consists of 8 turns of wire, each of area A = 0.09 m2 & the total
resistance of the wire is 12 Ω. The loop rotates in a 0.5 T magnetic field at a constant
frequency of 60 Hz.

(a) Find the maximum induced emf.
(b) What is the maximum induced current ?

b) An automobile generator produces 12.0 V when turning at 500 rev/min. What
potential difference will it produce at 1200 rev/min?

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5.3 Self Inductance

10. (a) Define what is meant by self-induction. What is meant by a
self- inductance of 2H.

(b) Write an equation that relates the induced emf,ξ self inductance, L and current, I.

11. (a) A coil of 200 turns has a length 5.0 cm and a cross–sectional area 4.0 cm2. Calculate the self-
inductance of the coil.
(Permeability of medium inside coil = 5000μo)

(b) If the self- inductance, L of solenoid. For solenoid l  60cm , A  6cm2 and L =150 m H.

Determine :
i. the number of turns in the solenoid
ii. the number of turns per unit length
iii. the induced emf in the solenoid if the current increase from 0 to 4 A in 0.06s.
iv. the rate of change of magnetic flux in the solenoid.

5.4 Energy stored in Inductor

12. A 400 turns solenoid has a cross sectional area 1.81×10-3 m2 and length 20 cm carrying a
current of 3.4 A.

(a) Calculate the inductance of the solenoid
(b) Calculate the energy stored in the solenoid
(c) Calculate the induced emf in the solenoid if the current drops uniformly to zero

in 55 ms.

5.5 Mutual Inductance

13. Two coils, X & Y are magnetically coupled. The emf induced in coil Y is 2.5 V when the
current flowing through coil X changes at the rate of 5 A s-1. Determine:
(a) the mutual inductance of the coils
(b) the emf induced in coil X
if there is a current flowing through coil Y which changes at the rate of 1.5 A s-1.

5.6 Back emf

14. (a) A motor in normal operation carries a direct current of 0.850 A when connected to a 120 V
power supply. The resistance of the motor windings is 11.8 Ω. While in normal operation,
what is the back emf generated by the motor?

(b) At what rate will internal energy be produced in the windings in this case? (Most motors
have a thermal switch that will turn off the motor to prevent overheating when this occurs.)

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Chapter 6
Geometrical Optics

(1 Hours)

6.1 Reflection at a spherical surface
6.2 Refraction at spherical surfaces
6.3 thin Lenses

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