A tightly wound solenoid with radius R and length >>R is composed of N turns of

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A tightly wound solenoid with radius R and length ℓ >>R is composed of N turns of conducting wire. The solenoid carries a slowly varying current I (t) and experiences a voltage drop V (t) over its length. Show that

where Eis the average electric field along the solenoid axis and Eθ is the tangential electric field at the surface of the solenoid.

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