Electromagnetic induction
Chapter
6 1
Chapter
Faraday’s experiment
Faraday discovered electromagnetic induction.
In 1831, Faraday used the experiment below to test his hypothesis
that a magnetic field would induce an electric current.
When the current was steady, the galvanometer indicated no induced current, but when the switch was
turned on or off – and only then – was an induced current measured.
Changing the current produces a variation in the magnetic field associated with the current.
A changing magnetic field therefore induces an electromotive force (EMF)
which produces an induced current.
induced electromotive force
A current is induced when a magnet is moved towards a coil,
causing the magnetic field through the coil to increase.
The induced current is of opposite sign when the magnet is moved awaySfrom the coil, when the
magnetic field through the coil decreases.
No current is induced if the magnet does not move relative to the coil.
It is the relative motion which induces current: for example, a current is also induced if the magnet is
held steady and the coil is moved.
Faraday and Neumann’s law of induction
The induced EMF in a wire loop is proportional to the rate of change of the
magnetic flux through the surface associated with the loop.
fem  
r
 B



t
r
where (B) is the flux
through the surface.

r
r r
 B B A

where θ is the the angle
between
r
r
A
the magnetic field vector B and the vector ,
normal to the loop of area A.
The unit of magnetic flux is the weber, Wb: 1 Wb= 1 T ∙ m2.
The magnetic flux
through a loop
is proportional to the total
number of magnetic field lines
passing through the loop.

   BAcos 

Lenz’s law
The current produced by an induced EMF moves in such a direction
that the magnetic field it produces attempts to restore the changed field to its
original value.
An induced EMF is always in a direction that opposes the original change in flux
that caused it.
magnitude of
the external
magnetic
field, B
flux of the
external
magnetic
field, B
external
magnetic
field
B lines
increase
r
 (B)  0
more
numerous
opposite
to B
r
 (B)  0
less
numerous
same
as B

decrease

direction of the induced magnetic field, Bi
electromotive force and the Lorentz force
By moving a conducting rod inside a magnetic field, the electrons in the rod
experience Lorentz forces.
The direction of the Lorentz force Fl is perpendicular to the rod velocity v (and hence to the velocity
gained by free electrons in the rod) and to the magnetic field B.

This will cause a movement
of the free electrons and as consequence a potential
difference at the ends of the rod which acts as an electric generator.
This is a qualitative explanation of induced EMF.
force on a rod moving in a magnetic field
Moving a rod, that is part of a conducting loop,
inside a megnetic field, generates current.
To make the rod move to the right at speed v,
an external force needs to be applied on the rod
to the right, as the system attempts to restore
the changed flux (Lentz’s law).
The external force needs to be equal and opposite to the magnetic force F = IB l .
The induced current is equal to the change in the flux,
divided by the resistance R of the loop.

I
Bl v
R
Hence the external force to be applied is:

B2 l 2 v
F
R
alternating current
The motion of a metal loop within a magnetic field causes electrons to move
in the metal, under the influence of Lorentz forces, thereby generating a current.
If the loop is rotating with a constant velocity in a uniform magnetic field,
an alternating current is generated
The voltage varies sinusoidally
with time:


 
V  V0 sin 2f t  V0 sin t

where V0 is the peak voltage,
i.e. the amplitude of the
oscillation,
f is the oscillation frequency
and ω is the angular frequency,
i.e. ω = 2πf.
I

 
 
V V0
 sin t  I0 sin t
R R
transformers and power transmission
A transformer consists of two coils, either
twisted around or linked by an iron core.
A changing EMF in one coil induces an EMF
in the other. The ratio of the EMFs is equal to
the ratio of the number of turns in each coil:
VS N S

VP N P
Due to energy conservation,
if there are no losses, the power input

is the same as output and the ratio of the currents is equal
to the inverse of the ratio of turns.
I S NS

I P NP
Transformers
 work with
alternating current, so it is
possible for power transmission
lines to work at high voltage,
there by minimising power
loss, and then step the voltage
down for use in the home.
the Earth’s magnetic field
Moving electric charges generate magnetic fields and
varying magnetic fields move charges.
In the core of the Earth, metal ions are in movement,
dragged by Earth’s rotation.
Metal ions in movement give rise to a current
that produces the Earth’s magnetic field.
The direction of the Earth’s magnetic
field is titled
by 11.5 degrees with respect
to its rotational axis.
The Earth's magnetic field
can be approximated as a dipole field
at the Earth’s surface.
However due to solar winds
it is distorted further out.