CHAPTER 5 Magnetism _ Electromagnetic Induction

EXERCISE 5:

A flat surface with area 3.0 cm2 is placed in a uniform magnetic
field. If the magnetic field strength is 6.0 T, making an angle 30°
with the surface area, find the magnetic flux through this area.

5.4 Induced emf

• a) State Faraday’s law.

• b) Use Faraday’s law. ,. = − Φ


• c) State Lenz’s law.

• d) Use Lenz’s law to find the direction of induced current.
• e) Use induced emf in:

• i. in straight conductor, =

• ii. in coil, = − , =


Electromagnetic Induction

Electromagnetic Induction is the production of induced e.m.f or
induced currents whenever the magnetic flux through a loop, coil or
circuit is changed.

The meaning of changing in magnetic flux : a

(1) there is a relative motion of loop & magnet field
lines are ‘ cut ‘ Figure 26(a).
(2) the number of magnetic field lines passing through

a coil are increased or decreased figure 26(b).

A bar magnet being pushed into a coil. It is known b
that while the magnet is being pushed, the Figure 26
galvanometer shows a deflection showing that a
current is induced in the coil.
If the magnet is pulled out, the galvanometer needle
deflects in opposite direction showing that the
induced current is in opposite direction.

Consider the experiment below:

a b c

When there is no Figure 26 Moving the magnet
relative motion away from the loop
between the magnet Moving the magnet decreases the number of
& the loop, G shows toward the loop magnetic field lines
no deflection. No increases the number passing through the
induced current. of field lines passing loop. The induced
through loop. The G current is now in
needle is deflected opposite direction.
indicating an induced
current is produced.

From the experiments, it can seen that e.m.f is induced only
when the magnetic flux through the coil change.

No change in magnetic flux,
electromagnetic induction
cannot occur.

It was further shown that induced e.m.f increase when:
(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.

Faraday’s Law of Induction

The induced emf for a given loop is found to be
proportional to the rate at which the magnetic flux
changes with time.
express mathematically:

 = − d

dt

* minus sign (–) indicates that the induced emf opposes the
change in magnetic flux ( Lenz’s law )

Lenz’s Law
An induced current always flow in a direction that
opposes the change in magnetic flux that causes it.

Figure 27

The induced current produced a north pole to oppose
the incoming north pole Figure 27.

SN
NS

Figure 28

Check your understanding
The solenoid in figure is moved at
constant velocity towards a fixed bar
magnet. Using Lenz’s law, determine the
direction of the induced current through
the resistor.
Movement of solenoid

ab

North pole

When solenoid bring towards South pole
magnet bar, it experience an
increasing in flux. Movement of solenoid
Flux change, current induced.
Lenz’s law, direction of current N
induced opposes the change.
The right end of solenoid must Iin d u ced Iin d u ced
form north pole.
a b
to the RIGHT (a to b)

According to Faraday’s Law :

A changing magnetic field can produce an electric current.

Magnetic flux, ø change→ induced an e.m.f.
From: Φ = NBA cos θ
→ When B, A or θ change, magnetic flux, ø

change
→ e.m.f or current induced.

Direction of induced emf opposes the changes
that causes it → Lenz law.



1. Induced e.m.f in a straight conductor moving through a
magnetic field.

As a conductor is moved through a magnetic field, current is
induced and the bulb is lightened up.

Calculation of emf induced in straight conductor.
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 Figure 29.

Figure 29 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 (BA cos )

dt

Knowing that B is constant Substitute (2) into (1):

and the angle between  = − Blv

normal of plane with B is 0° , dA indication of the direction of the
thus we have: induced emf ( Lenz’s Law )
 = − B (1)
dt In general form :
As the rod is pulled, the
The magnitude of the e.m.f. induced is
area of the circuit
 = Blv sin 
increases by an amount dA = l dx
where
At constant speed, the B : magnetic field strength
distance traveled by the l : length of the conductor
v : velocity of conductor
rod in a time interval dt is dx = v dt θ : angle between B and v

Thus we have : dA = l v dt

dA = l v (2)
dt

Direction of induced current flowing thought the conductor
can be determined using Right Hand Rule Figure 30.

Iinduced

Figure 30

induced current flows from b → a.

2. Induced e.m.f in a plane coil
(a) By changing area in magnetic field

Initial Final

Figure 31

Stretching the coil reduces the area of the coil → magnetic
flux through coil is decreased.

From: Magnetic Flux, ø = NBA cos θ
A↓ ø↓

As flux change → an e.mf is induced

An emf (voltage) & current are induced in the coil.

According to Faraday’s Law :

 = − N d = − d (NBAcos )

dt dt

( * B is perpendicular to the plane of coil →θ=0° ; cos 0 = 1 & magnitude of
B remain constant, coil with N number of turn)

 = − NB dA

dt

(b) By changing magnetic field strength. B
As the magnetic field strength, B is increasing or
decreasing with time, the magnetic flux through the area
changes, therefore induces an emf in the coil.

According to Faraday’s Law

 = − N d = − d (NBAcos)

dt dt

( * B is perpendicular to the plane of coil, A
constant & coil with N number of turn)

 = − NA dB

dt

Example 6:

The flexible loop has a radius of 12 cm and is in a magnetic
field of strength 0.15 T. The loop is grasped at point A and B
and stretched until its area is nearly zero. If it takes 0.20 s to
close the loop, find the magnitude of the average induced emf
in it during this time.

× ××××
× × ×A × ×
× ××××
× ××××
× ××××
× ××××
× ××××
× ××××

B

Solution : × Final × ×
Apply Faraday’s law: × ×× × ×
× × ×A × ×
 = − d = − B dA × ×× × ×
× ×× × ×
dt dt × ×× × ×
= − B ( Afinal − A )initial × ×× × ×
× ×× × ×
t ××

= − B (0 −  r 2 ) B

t

= − (0.15) (0 −  (0.12) 2 ) = 3.4 10 −2 V

0.20

EXERCISE 6:

A circular coil has 200 turns and diameter 36 cm. the resistance
of the coil is 2.0 Ω. A uniform magnetic field is applied
perpendicularly to the plane of the coil. If the field changes
uniformly from 0.5 T to 0 T in 0.8s.

a. Find the induced e.m.f. & current in the coil while the field is
changed.

b. Determine the direction of the current induced.

Example 7:
Consider the arrangement shown in figure.

Assume that R = 6 Ω, L = 1.2m & a uniform 2.50 T magnetic
field is directed into the page. (a) At what speed should the
bar be moved to produced a current of 0.5A in the resistor.
(b) what is the direction of the induced current ?

Solution :  = Blv sin 
(a) Using : IR = Blv sin 
v = IR = 0.5(6)

Bl sin  2.50(1.2) sin 90

v = 1 m s−1

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