Faraday's Law of Induction: Applied Physics FALL-2016

Faraday’s Law of Induction
APPLIED PHYSICS
FALL-2016
Faraday’s Law
• This chapter explores the effects produced by magnetic
fields that vary in time.
• Michael Faraday (1831) showed that an emf can be
induced in a circuit by a changing magnetic field.
Induced EMF
when a magnet is moved near

a wire loop of area A, current
Variable ΦB
(increasing) flows through that wire without
any batteries! ;
moving a magnet means
Constant ΦB changing the B-field through
the loop area  the magnetic
flux changing
Variable ΦB
(decreasing)
Induced EMF
The needle deflects momentarily when the switch is closed;

initially (the instant of closing switch), the magnetic field
increases during a certain very small period of time (the
needle deflects) until B-field becomes steady (the needle
goes back to zero)
Magnetic Flux
Magnetic flux is used

in the calculation of the
induced emf.
The emf induced in a circuit is directly proportional to the

time rate of change of the magnetic flux through the circuit.
d B
E 
dt
where,  B   B.dA
d B
For N loops, E  N
dt
d B
E   BA cos 
d
E 
dt dt
To induce an emf we can change over
time if the following:
•the magnitude of B
•the area enclosed by the loop
•the angle between B and the normal
to the area
•any combination of the above
Way to Induce an emf in a Coil
B-field ┴ to the plane.

B-field changes linearly from 0 to 0.50 T in square coil
N=200 turns
0.80 s.
What is the magnitude of the induced emf in
the coil while the field is changing?
18 cm
The induced
emf is
B-field
At t = 0 s, ΦB = 0 (no magnetic field) A=(0.18 m)² = 0.0324 m2
At t = 0.8 s, ΦB = B.A = BAcos0
= BA= (0.50 T)(0.0324 m²) = 0.0162 T.m²
Lenz’s Law
The polarity of the induced emf is such that it tends to produce a
current that creates a magnetic flux to oppose the change in
magnetic flux through the area enclosed by the current loop.
As the bar is slided to the
right, the flux through the
loop increases.
This induces an emf that
will result in an opposing
flux.
Since the external field is into
the screen, the induced field
has to be out of the screen.
Which means a
counterclockwise current
Energy Considerations
Suppose, instead of flowing counterclockwise, the induced current flows
clockwise:
Then the force will be towards the right
which will accelerate the bar to the right
which will increase the magnetic flux
which will cause more induced current to flow
which will increase the force on the bar
… and so on
the system would acquire energy with no input of energy.
All this is inconsistent with the conservation of energy

Motional EMF
• When B changes and the conductor is stationary  induced emf
• When a conductor moves through a constant magnetic field
motional emf,
As the wire moves, FB  qv  B  charges moves in the direction of FB and

leaves positive charges behind.
As they accumulate on the bottom,
an electric field is set up inside.
In equilibrium,
FB  FE Voltage drop across the

conductor
qvB  qE
E  vB
V  El  Blv
a potential difference is maintained between the ends of the conductor as long as the
conductor continues to move through the uniform magnetic field.
If the moving conductor is part of a closed conducting
path (closed circuit of resistance R).
The area enclosed by the circuit is A = lx
 B  BA  Blx
d B
E  
d
Blx    Bl dx
dt dt dt
E  Blv E Blv
I 
R R
If the bar is moved with constant velocity,
Fapp  FB  IlB
( Blv)lBv B 2 l 2 v 2 E 2
P  Fapp v  IlB v   
R R R
The mechanical power delivered by the external
force is:
Compare this to the electrical power in the

light bulb:
Therefore, mechanical power has been

converted directly into electrical power.
Generators and Motors
An electric generator converts mechanical energy

into electric energy:
An outside source of
energy is used to turn
the coil, thereby
generating electricity.
The induced emf in a rotating coil varies
sinusoidally:
An electric motor is exactly the opposite of a
generator – it uses the torque on a current loop to
create mechanical energy.
Eddy Currents
Induced EMF and E’Field
Summary
• Faraday’s law of induction  induced emf
• conducting bar of length l moves at a velocity v

through a magnetic field B 
motional emf induced in the bar
• The applied force to keep constant v is l 2 B 2v

Where R is resistance connected to moving bar Fapp  FB  IlB 
R
• Lenz’s law states that the induced current and induced emf in a conductor
are in such a direction as to set up a magnetic field that opposes the
change in the magnetic flux
• A general form of Faraday’s law of induction is
Which implies induced E-field is not conservative

BA  0
N
0.250
 0.5V
First we need to find the change in the ΦB
of the solenoid
Which is the same flux that change in the coil
But, =
Please do solved examples at
your own

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Faraday’s Law of Induction

when a magnet is moved near

The needle deflects momentarily when the switch is closed;

Magnetic flux is used

The emf induced in a circuit is directly proportional to the

B-field ┴ to the plane.

which will accelerate the bar to the right

which will increase the magnetic flux

which will cause more induced current to flow

which will increase the force on the bar

the system would acquire energy with no input of energy.

All this is inconsistent with the conservation of energy

As the wire moves, FB  qv  B  charges moves in the direction of FB and

FB  FE Voltage drop across the

Compare this to the electrical power in the

Therefore, mechanical power has been

An electric generator converts mechanical energy

• conducting bar of length l moves at a velocity v

• The applied force to keep constant v is l 2 B 2v

Which implies induced E-field is not conservative

Which is the same flux that change in the coil

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