Chapter 4 Magnetism SE

CHAPTER 6 : MAGNETIC FIELD
( 7 HOURS )

Terminology :

1. Magnetic field : Medan magnet.
2. Pole : Kutub.
3. Flux density : Ketumpatan fluks.
4. Magnetic force : Daya magnet.
5. Biot-Savarts law : Hukum Biot-Savart.
6. Drift velocity : Halaju hanyut.

Introduction :

1. The existence of magnetic interactions was already known by the 3rd century in
China. Even then it was understood that some metals could attract iron ore filings
from some distance.

2. Magnets are made from substances known as magnetite and magnetic pyrite. The
names are derived from the name is the city of Magnesia in Asia Minor.

Magnetic Field : JOTTING
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1. Every magnet generates a magnetic field around itself.

Magnetic field, B refers to a three dimensional field (region) around a magnetic
body or a current-carrying conductor where the force can be experienced.

Magnetic field is also known as ‘flux density’.

2. The magnetic properties of a magnet are concentrated at both ends called the
north (N) and south (S) poles.

3. Magnetic field, B is a vector quantity with SI unit of Tesla, T.

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Magnetic Field Lines :
1. Pattern of magnetic field is represented by the so-called ‘magnetic field lines’.

Natural methods can be used to observe the magnetic field pattern :
a. needles of a compasses.
b. pieces of iron (known as iron filings).

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Note : The direction of the magnetic field is determined by the north pole of the
magnetic needle.

2. Sources of magnetic field :
a. Bar magnet (Direction : N → S).
b. Current-carrying conductor (Direction : right hand rule or corkscrew rule).
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© Physics Teaching CoursewareBar magnetHorseshoe magnet
JOTTING
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Current-carrying conductor Inwards the plane Outwards the plane

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Note : A freely suspended magnet aligns itself in a particular direction. This
direction roughly run parallel to the earth’s north/south axis and also
implies that the earth itself is a giant magnet.

axis axis

north pole earth magnetic

N field

S JOTTING
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south pole

Earth has a week magnetic field caused by the electrical current flowing in its core.
The earth’s magnetic field gradually changes in magnitude and direction over time
and acts very much like a giant bar magnet.

3. Properties of the magnetic field lines :
a) The field lines never cross or split each other.
b) There are no two or more of field lines at the same point.

4. Properties of uniform magnetic field :
a) The magnetic field lines are in straight lines.
b) The magnetic field lines are parallel one another.
c) The magnetic field lines are at the same distance one another.

B

If the field lines are close, the magnetic field is strong and vise versa.

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Magnetic Flux :

1. Magnetic flux, φ measures the number of magnetic field lines passing through a
coil of area, A whose normal and makes an angle, θ with the magnetic field, B.

Or φ = B • A

Or φ = BA cosθ …..(6.1a)

θ

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Note : Unit for magnetic flux is Tm2 or normally known as Webber, Wb.

If a coil has N turns, the flux linkage is the sum of the fluxes through each coil. JOTTING
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φ = NBA cosθ …..(6.1b)

Magnetic Field produced by Electrical Current :

1. Biot-Savart’s Law :
Biot-Savart’s Law is used to determine the magnetic field (or flux density)
generated by a conductor of any shape at any point in the field.

Biot-Savart’s Law states that :

“The magnetic field, dB at a point generated by segment dL of a conductor

carrying a current of I is defined by :

dB ∝ (I)(dL)(sin θ)
r2

Or dB =  µo  IdL sin θ
4π r2

where r = distance between the point to the conductor.
θ = angle between r and I
µo = permeability of free space = 4π x10-7TmA-1.

2. Ampere’s Law :
Ampere’s Law is used to calculate the magnetic field when the distribution of the
current- carrying conductors is symmetrical.

Ampere’s Law can be defined through the following expression :

∫ B • dL = µoIc

∫Or BdL cos θ = µoIc

where IC = total current enclosed by a closed loop.
θ = angle between B and dL.

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Examples of B for several symmetrical conductor :

a) Magnetic field at the centre of the coil with N turns and radius R (Figure 1) :

B = µoNI …..(6.2)
2R

b) Magnetic field on the axis of a solenoid which has n turns per meter
(Figure 2) :

B = µonI …..(6.3)

c) Magnetic field at a long straight wire (Figure 3) :

B= µoI …..(6.4)
2πr

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JOTTING
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Figure 1 Figure 2 Figure 3

Magnetic Force :

1. Magnetic Force, FB refers to the force which is produced by the magnetic field, B
as a result of :
d) a moving charged particle across the magnetic field.
e) a flowing electric current across the magnetic field.

2. Magnetic force (just like other type of forces) is a vector quantity. The direction of
magnetic force can be determined using ‘Fleming Left hand Rule’ as follow :

F

B
θ

θ v or I

The direction of magnetic force is always perpendicular to the direction of v (or I)
and B.

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Force on a moving Charged Particle in a Magnetic Field :

1. When a charge particle of charge, q is moving at angle θ with the direction of a
uniform magnetic field, B the force produced is given by :

F = qv X B

Or F = qvB sinθ …..(6.5)

Where q = magnitude of charge.

v = velocity of the particle.
θ = angle between the direction of v and B.

Example :

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Note : Since the direction of the magnetic force depends on the direction of
the velocity (always perpendicular each other), then the charge will
undergo a circular motion.

Force on a current carrying Conductor in a Magnetic Field :

1. When a conductor which carries a current of intensity I is placed in a uniform
magnetic field, B the forced produced is given by :

F = IL X B

Or F = ILB sinθ …..(6.6)

Where I = intensity of current flowing through the conductor.

L = length of the conductor.
θ = angle between the direction of I and B.

Example :

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Example :
A wire of length 15.0 cm is placed at an angle of 30o in a uniform magnetic field of 20 mT.
If the current in the wire is 2.5 A, what is the magnetic force acting on the wire.

Forces between Current-Carrying Conductors :
1. Consider two infinitely long parallel conductors placed at a distance d from one

another, which carry currents I1 and I2 respectively in the same direction.

© Physics Teaching CoursewareFigure 1 Figure 2 Figure 3
JOTTING
SPACEFigure 2 :
The field generated by conductor (1) which extends over the area

that contains conductor (2) at distance d is :

B1 = µ oI1
2πd

Thus, the conductor (2) is affected by a magnetic force as follow :

F2 = I2LB1sinθ where θ = 90o

Or F2 = I2L  µ oI1 
2πd

By using Fleming Left hand Rule, the force is directed towards conductor (1).

Figure 3 : The field generated by conductor (2) which extends over the area

that contains conductor (1) at distance d is :

B2 = µ oI2
2πd

Thus, the conductor (1) is affected by a magnetic force as follow :

F1 = I1LB2sinθ where θ = 90o

Or F1 = I1L  µ oI2 
2πd

By using Fleming Left hand Rule, the force is directed towards conductor (2).

Conclusion :

a) Two parallel infinitely long conductors carrying current in the same
directions attract one another.

b) The magnitude of forces F1 and F2 are identical, but their directions are
opposite.

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2. Consider two infinitely long parallel conductors placed at a distance d from one
another, which carry currents I1 and I2 respectively in the opposite direction.

© Physics Teaching CoursewareFigure 1 Figure 2 Figure 3
JOTTING
SPACEFigure 2 :
The field generated by conductor (1) which extends over the area

that contains conductor (2) at distance d is :

B1 = µ oI1
2πd

Thus, the conductor (2) is affected by a magnetic force as follow :

F2 = I2LB1sinθ where θ = 90o

Or F2 = I2L  µ oI1 
2πd

By using Fleming Left hand Rule, the force is directed opposite to conductor (1).

Figure 3 : The field generated by conductor (2) which extends over the area

that contains conductor (1) at distance d is :

B2 = µ oI2
2πd

Thus, the conductor (1) is affected by a magnetic force as follow :

F1 = I1LB2sinθ where θ = 90o

Or F1 = I1L  µ oI2 
2πd

By using Fleming Left hand Rule, the force is directed opposite to conductor (2).

Conclusion :

a) Two parallel infinitely long conductors carrying current in the opposite
directions repel one another.

b) The magnitude of forces F1 and F2 are identical, but their directions are
opposite.

Example :

A wire of length 25.0 cm carrying a current of 1.8 A is placed at a distance of 4.0 cm
parallel to another long wire carrying a current of 2.4 A in vacuum. Calculate the magnetic
force acting on the first wire.

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Definition of Ampere :

1. The unit of electric current is ampere. The definition of 1 Ampere in the SI system
was based on the magnetic interaction between current-carrying conductors.

2. Consider two infinitely long straight conductors are placed 1 meter apart (d = 1m)

and they are carrying currents of magnitudes 1 Ampere (I1 =I2 = 1A), then :

F = µ oI1I 2
L 2πd

= (4πx10 −7 )(1)(1)
2π(1)

= 2 x10-7 Nm-1

Therefore, 1 Ampere is defined as :
= The direct electric current which, when flowing through two parallel infinitely long

straight conductors of negligible circular cross-section, placed one meter apart in
free space, will produce a force of magnitude 2 x10-7 N on every meter of their
lengths.

Torque on a Coil in a Magnetic Field JOTTING
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1. Consider a rectangular coil (loop) of wire with side lengths a and b which turns
about axis PQ as shown in the below figure.

The coil is situated in a uniform magnetic field, B and the plane of the coil
makes an angle θ with the direction of the magnetic field. Besides, a current I is

flowing round the coil.

BB F1

I
F4

B
I A φθ

B bB

aI
I
F3 F2

Figure : Plan view.

2. As a result, based on the left-hand rule, forces F1, F2, F3 and F4 produced with
certain direction as shown in above figure.

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3. The net (resultant) force on the coil equals zero. However, the net torque is not
zero (due to F1 and F3 which are acting b/2 apart of axis PQ).

B

A B I⊗ F1

rotation φθ φ b sinφ rotation
• 2

B b sinφ
2
b
F3 2

I

Figure : Side view.

The magnitude of the net torque about axis PQ : …..(6.7a)

∑ τ = IABsinφ

where mathematically, φ = 90o - θ. JOTTING
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For a coil of N turns, the above equation can be written as :
…..(6.7b)
∑ τ = NIABsinφ

The net torque becomes maximum when φ =90° or θ = 0°, and the equation is :

∑ τ = NIAB …..(6.7c)

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A Moving-Coil Galvanometer

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1. A galvanometer consists of a coil of wire suspended in the magnetic field of a
permanent magnet. The coil is rectangular and consists of many turns of fine
wire as shown in figure above.

2. When the current flows through the coil, the magnetic field exerts a torque on JOTTING
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the coil as given by :

∑ τ = NIAB

3. This torque is opposed by a spring which exerts a torque, τs given by

∑ τS = kθ

where k = torsional constant (torque per unit radian).
θ = rotational angle of the coil ( in unit radian).

4. The coil and pointer will rotate only to the point where the spring torque balances
the torque due to magnetic field, thus :

or finally, ∑ τ = ∑ τS

I =  k θ
 NAB 

5. Thus, I is proportional linearly to the deflection of the wire, θ which shown with the
pointer of the meter on a scale.

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The DC Electrical Measuring Instruments (Motor)

1. A motor is an instrument that converts electrical energy to mechanical energy.

A motor works on the same principle as a galvanometer, except that there is no
spring so the coil can rotate continuously in one direction.

2. When a current flows in the coil in a so-called ‘radial magnetic field’, a net torque
is produced which causes the coil to rotate with magnitude :

∑ τ = NIAB

commutator C2 B2 fixed brush JOTTING
rotates contact SPACE

B1 C1 © Mohd. Hazri @ kmph

3. The commutators C1 and CF2igar7e.9aalso rotating with the coil but the brushes B1
and B2 are remain stationary with the circuit.

When the coil rotates half revolution (180°), each commutator changes its
connection to the other brush where C1 touches B2 and C2 touches B1.

This arrangement will cause the direction of the current through the coil to be
reversed after every half revolution and ensures that the direction of the torque is
always the same. As a result, the coil can turn continuously.

Motion of Electric Charges in Magnetic and Electric Field :

1. Motion of Electric Charges, q in Magnetic Field, B :
A particle with a charge q which is moving in the magnetic field, B with a velocity, v
is affected by a magnetic force perpendicular to the velocity, which curves the path
of the particle.

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As we know, motion in circular path produces so-called ‘centripetal force’, FC
directed to the centre of the circle. Thus :

FC = FB
Or qvB = mv 2

r

Therefore, r = mv …..(6.8)
qB

Period of the motion :

T = 2πm …..(6.9)
qB

Note : It shows that the period is not depends on the velocity.

2. Motion of Electric Charges, q in Magnetic Field, B and Electric Field, E :

A charge moving with velocity v in the presence of both electric field, E and JOTTING
magnetic field, B will experience : SPACE

Electric force : FE = qE
Magnetic force : FB = qvB sinθ

Therefore, by using vector operation,
the total force :

∑F = FE + FB

and normally known as ‘Lorentz Force’.

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Determination of q/m :

1. The knowledge of the laws of motion for charged particles in electromagnetic fields
makes it possible for us to study the properties of the particles.

We will discuss a typical experiment that enables us to determine the ratio of
particle charge to particle mass.

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The potential difference (voltage), V between the cathode and the anode
accelerates the charged particles by providing them with kinetic energy :

1 mv 2 = qV JOTTING
2 SPACE

Or v = 2qV …..(i)
m

As we discussed, a charged particle moving with velocity v in the presence of both
electric field, E and magnetic field, B will experience the Lorentz force :

The charged particle will only pass through the selector without undergoing any
deflection if :

FE = FB

Or qE = qvB

Thus v= E …..(ii)
B

Combination of equations (i) and (ii) : …..(6.10)
q = E2
m 2VB2

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