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Lecture 9
Electromagnetic Induction
Chapter 20.1  20.4
Outline
• Induced Emf
• Magnetic Flux
• Faraday’s Law of Induction
Electromagnetic Induction
If an electric current produces a magnetic field, then a
magnet should be able to generate an electric current.
A current is produced in a wire when there is relative
motion between the wire and a magnetic field.
Such a current is called an induced current (emf).
The effect is called electromagnetic induction
(discovered by Michael Faraday in the XIX century).
The strength of the current depends on the magnetic
field strength and the wire’s speed.
Magnetic Flux
The emf is induced by the magnetic flux, rather
than the magnetic field.
Magnetic flux is a measure of the total number of
magnetic lines passing through an area.
Consider a loop of wire in the presence of a uniform
magnetic field B. If the loop area is A, then the
magnetic flux B through it is defined as:
B = BA = BA cos 
B is the component of
B, perpendicular to the
plane of the loop
Faraday’s Law of Induction
The induced emf exists only when there is a relative
motion between the magnet and the circuit.
Faraday’s law states that the instantaneous induced
emf equals the rate of change of magnetic flux
through the circuit.
If a circuit has N loops and the flux through each
loop changes by the amount of B during
interval of time t, the average emf ℇ induced in
the circuit during this time is:
ℇ =  N B/t
Polarity of the Induced Emf
The induced emf produces an induced current.
The induced current produces its own magnetic field.
The induced magnetic field opposes the change of
the external magnetic field.
The polarity (direction) of the induced emf is
determined by Lenz’s law.
Motional Emf
Let us consider an application of Faraday’s law to a
conductor of length l moving at a constant velocity
v through a uniform magnetic field.
Picture
qE = qvB
E = vB
F = qvB
 Magnetic force on
electrons in the conductor
E is the electric field induced in the
conductor
E is uniform  the potential difference
across the conductor ends V = E l
Summary
• The phenomenon of electromagnetic induction
refers to appearance of an electric field under
influence of a magnetic field.
• Faraday’s law connects the induced emf and
time change in the magnetic flux.
• Lenz’s law defines the polarity of the induced
emf
• Motional emf is an emf produced in a moving
conductor under influence of a magnetic field.