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# F16 PH333 7.2.1-7.2.2

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## Richard Datwyler

on 10 December 2018

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#### Transcript of F16 PH333 7.2.1-7.2.2

Electromagnetic Induction
7.2.1 Faraday's Law
7.2.2 Induced Electric Field
Faraday's Discovery
1. Pull the loop out of the field - current
2. Pull the field away from the loop - current
3. Turn down the B field - current
Relativity says the first two must be the same (Faraday didn't know this)
The second one seems to break Lorentz force (no motion, no force, current won't move)
Faraday's solution... Faraday's law: Changing magnetic fields induce electric fields
Technically the second two experiments resulted in the same thing. They had changing magnetic fields that induced E fields.
Notes
Often we associate Faraday's law to be
and as we see from these experiments, the flux can change via different physical means. Only two of which are from Faraday's assertion.
And Nature resists change.
Point is, changing fields, create other fields.
Long solenoid of radius
a
is AC driven, and results in a field. A single loop with radius
a/2
and resistance
R
is put inside coaxial to it. Find induced current at function of time.
first -
then -
finish -
We often note the result as an induced Current, but really it is an induced Electric field
Induced Electric Field
recall we found B from currents
The electric field must be specified by both as well.
but the curl is not enough, also need divergence.
if there is no charge density then divergence is
We can find the curl of E with the same trick as B.
A long solenoid with radius
a
and
n
turns per unit length caries a current I(t) azimuthally. Find the E field a distance s from the axis.
finish
outside-
finish
inside-
start -
We will call it there, and pick up on inductance next time
"I don't understand how pulling the loop was physically different from pulling the magnet away. Can you go over question 3 on the quiz?"
"Can you explain Lenz's Law a little more? Is it always in the direction opposite the B-field?"
"Are the induced electric fields considered non-conservative since how the divergence is zero, and the curl is non zero?"
"Lenz's law is related to Faraday's law in what way? (magnitude or direction)
Full transcript