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10. Electromagnetic Induction
Faraday’s law
If a magnetic field changes in time there is an
induced electric field.
In differential form, the field equation is
B
E  
t
which is called Faraday’s Law.
In integral form,
d
CE  d l   dt
where  is the magnetic flux through any surface
with boundary curve C.
(Why are the two equations equivalent?)
G L Pollack and D R Stump
Electromagnetism
1
Lenz’s law
The direction of the induced electric field in
electromagnetic induction opposes the change of
magnetic flux; i.e., if a conductor is present then the
induced current produces a magnetic field in the direction
tending to maintain the flux.
Self-inductance
A current I in a conducting loop creates a magnetic field.
The flux through the loop is proportional to the current,
 = LI . The constant of proportionality L is the selfinductance, which depends on the geometry of the loop.
If I changes in time there is an induced emf around the
loop, which is by Faraday’s law   L dI dt
.
G L Pollack and D R Stump
Electromagnetism
2
Exercises
• Show that an LC circuit is an oscillator.
• Show that the energy in an inductor is
U  12 LI 2 .
• Show that the energy density of the magnetic field is
umag  B 2 20 .
G L Pollack and D R Stump
Electromagnetism
3