EP025 Lecture 4

CHAPTER 4 : MAGNETISM

6.0 INTRODUCTION

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.

Magnets are made from
substances known as magnetite
(Fe3O4) and magnetic pyrite.
The names are derived from the
name is the city of Magnesia in
Asia Minor.

CHAPTER 4 : MAGNETISM

6.1 MAGNETIC FIELD

Magnetic field, B (also known as
flux density) refers to a 3-D field
(region) around a magnetic body or
a current-carrying conductor where
the force can be experienced.

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

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

6.1 MAGNETIC FIELD

6.1 MAGNETIC FIELD

Magnetic field of some sources

6.1 MAGNETIC FIELD

Natural methods can be used to observe the magnetic
field pattern :

• needles of a compasses.
• pieces of iron (known as iron filings).

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

6.1 MAGNETIC FIELD

Physically, the pattern of magnetic field is represented
by the so-called ‘magnetic field lines’

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

6.1 MAGNETIC FIELD

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

Properties of uniform magnetic field :

• The magnetic field lines are in
straight lines.

• The magnetic field lines are
parallel one another.

• The magnetic field lines are at the
same distance one another.

6.1 MAGNETIC FIELD

EARTH MAGNETIC FIELD

A freely suspended magnet
bar 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.

6.1 MAGNETIC FIELD

EARTH MAGNETIC FIELD

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.

CHAPTER 4 : MAGNETISM

6.2 MAGNETIC FIELD PRODUCED BY CURRENT-CARRYING CONDUCTOR

Generally, there is no special
expression of magnetic field
produced by current-carrying
conductor.

Based on Biot-Savart’s law and
Ampere’s law, the expression
depends on the shape of the
conductor itself.

6.2 MAGNETIC FIELD PRODUCED BY CURRENT-CARRYING CONDUCTOR

MAGNETIC FIELD AT THE CENTRE OF COIL

Magnetic field at the centre
of the coil with N turns and
radius R :

6.2 MAGNETIC FIELD PRODUCED BY CURRENT-CARRYING CONDUCTOR

MAGNETIC FIELD AT THE CORE OF SOLENOID

Magnetic field on the axis of
a solenoid which has n turns
per meter ( n = N / l):

6.2 MAGNETIC FIELD PRODUCED BY CURRENT-CARRYING CONDUCTOR

MAGNETIC FIELD ALONG STRAIGHT ROD

Magnetic field at a long
straight wire :

6.2 MAGNETIC FIELD PRODUCED BY CURRENT-CARRYING CONDUCTOR

The direction of magnetic field
produced by current-carrying
conductor can be determined by
using Corkscrew Rule.

CHAPTER 4 : MAGNETISM

6.3 FORCE ON A MOVING PARTICLE IN A UNIFORM MAGNETIC FIELD

MAGNETIC FORCE

Magnetic Force, FB refers to the
force which is produced by the
magnetic field, B as a result of :
• a moving charged particle across

the magnetic field.
• a flowing electric current across

the magnetic field.

6.3 FORCE ON A MOVING PARTICLE IN A UNIFORM MAGNETIC FIELD

MAGNETIC FORCE

Magnetic force (just like other type of forces) is a
vector quantity where the direction can be determined

using ‘Fleming Left-hand Rule’.

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

6.3 FORCE ON A MOVING PARTICLE IN A UNIFORM MAGNETIC FIELD

When a charge particle of
charge, q is moving with

velocity v at angle  with the

direction of a uniform magnetic
field, B the force produced is
given by :

F = qv X B

6.3 FORCE ON A MOVING PARTICLE IN A UNIFORM MAGNETIC FIELD

If the charge moves

perpendicularly ( = 90o), the

charge eventually undergoes a
circular motion with radius R.

As a result, the magnetic force
contributes the production of
centripetal force.

6.3 FORCE ON A MOVING PARTICLE IN A UNIFORM MAGNETIC FIELD

If the charge moves at angle,

 < 90o, the charge eventually

undergoes a helical motion
with radius R.

If the charge moves parallel,

 = 0o, no force is produced.

The charge remain its original
linear motion.

CHAPTER 4 : MAGNETISM

6.4 FORCE ON A CURRENT-CARRYING CONDUCTOR IN A UNIFORM B

When a conductor of length L
which carries a current, I is

placed at angle  in a uniform

magnetic field, B the forced
produced is given by :

F = IL X B

&

QUESTION 1

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.

ANSWERS
3.75x10-3 N

CHAPTER 4 : MAGNETISM

6.5 FORCE BETWEEN 2 PARALLEL CURRENT-CARRYING CONDUCTORS

CASE 1 : SAME DIRECTION

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.

The magnetic field, B1 generated by
conductor (1) which extends over the
area that contains conductor (2) at
distance d is :

6.5 FORCE BETWEEN 2 PARALLEL CURRENT-CARRYING CONDUCTORS

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

F2 = I2LB1sin where  = 90o

or

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

6.5 FORCE BETWEEN 2 PARALLEL CURRENT-CARRYING CONDUCTORS

On the other hand, the magnetic field,
B2 generated by conductor (2) which
extends over the area that contains
conductor (1) at distance d is :

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

F1 = I1LB2sin where  = 90o

or

6.5 FORCE BETWEEN 2 PARALLEL CURRENT-CARRYING CONDUCTORS

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

Conclusion :
• Two parallel infinitely long conductors

carrying current in the same directions
attract one another.
• The magnitude of forces F1 and F2 are
identical, but their directions are
opposite.

6.5 FORCE BETWEEN 2 PARALLEL CURRENT-CARRYING CONDUCTORS

CASE 2 : OPPOSITE DIRECTION

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.

Conductor (1) and (2) are respectively
affected by a magnetic force :

6.5 FORCE BETWEEN 2 PARALLEL CURRENT-CARRYING CONDUCTORS

Using Fleming Left hand Rule, the
forces are directing away from each
conductor.

Conclusion :

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

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

6.5 FORCE BETWEEN 2 PARALLEL CURRENT-CARRYING CONDUCTORS

DEFINITION OF 1 AMPERE

Consider two infinitely long straight
conductors are placed 1 meter apart
(d = 1 m) and they are carrying currents
of magnitudes 1 Ampere (I1 = I2 = 1 A),
then :

6.5 FORCE BETWEEN 2 PARALLEL CURRENT-CARRYING CONDUCTORS

DEFINITION OF 1 AMPERE

Therefore, 1 Ampere is defined as :

“the direct electric current (DC) which,
when flowing through two parallel
infinitely long straight conductors of
negligible circular cross-section, placed
1 m apart in free space, will produce a
magnetic force of magnitude 2 x10-7 N
on every meter of their lengths.”

6.5 FORCE BETWEEN 2 PARALLEL CURRENT-CARRYING CONDUCTORS

&

QUESTION 2

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.

ANSWERS
5.4x10-6 N

CHAPTER 4 : MAGNETISM

.

6.6 TORQUE ON A COIL

Figure : Plan view. Consider a current-carrying
rectangular coil (loop) of N
turns with dimension a x b
which rotates about its axis is
situated in a uniform magnetic
field, B and its plane makes

an angle  with the direction

of the magnetic field.

As a result, F1, F2, F3 and F4 are produced in such
directions as shown in above figure.

Figure : Side view. 6.6 TORQUE ON A COIL

The resultant force = 0.
The resultant torque  0
(due to F1 and F3 which are
acting b/2 apart of the axis.

The magnitude of the
resultant torque :

where mathematically,
 = 90o - .

6.6 TORQUE ON A COIL

MOVING COIL GALVANOMETER

A galvanometer consists of an N
turns rectangular coil suspended
in the permanent radial magnetic
field.

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

…..(i)

6.6 TORQUE ON A COIL

MOVING COIL GALVANOMETER

This torque is opposed by a

spring which exerts a torque, s

given by :
…..(ii)

where :
k = torsional constant (torque

per unit radian).
= rotational angle of the coil

( in unit radian).

6.6 TORQUE ON A COIL

MOVING COIL GALVANOMETER

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

or finally :

Thus, I is proportional linearly to the deflection of the

wire,  which shown with the pointer of the meter

on a scale.

CHAPTER 4 : MAGNETISM

6.7 MOTION OF CHARGED PARTICLE IN MAGNETIC & ELECTRIC FIELD

A charge q which moves with velocity
v in the presence of both electric
field, E and magneticfield, B will
experience both electric force and
magnetic force :

FE = qE

FB = qvB sin

Therefore, the forces are balanced
out, then the resultant force
experienced by the charge = 0.

6.7 MOTION OF CHARGED PARTICLE IN MAGNETIC & ELECTRIC FIELD

Mathematically :

FE = FB

or qE = qvB sin

Therefore :
• the charge remains in its original

linear motion without
experiencing any deflection due to
the two forces.
• the motion does not depend on
the strength of the charge.