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G L Pollack and D R Stump Electromagnetism

1

10. Electromagnetic Induction

Faradays law

If a magnetic field changes in time there is an induced electric field.

In differential form, the field equation is

which is called Faradays Law.

In integral form,

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

2

Lenzs 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 self-inductance, which depends on the geometry of the loop.
If I changes in time there
is an induced emf around the loop, which is by Faradays law                          
.

G L Pollack and D R Stump Electromagnetism

3

Exercises

Show that an LC circuit is an oscillator.

Show that the energy in an inductor is                   
.

Show that the energy density of the magnetic field is

                           
.