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# Introduction to Electrodynamics (3rd Edition)

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ELECTRICITY AND MAGNETISM I HOMEWORK 14: GRIFFITHS 7.17,22,27,31,34 MIKE WININGER Problem 1 (Griﬃths 7.17: Current through a long solenoid.) . . A long solenoid of radius a, carrying n turns per unit length, is looped by a wire with reistance R. a) If the current in the solenoid is increasing at a constant rate ( dI dt = k ), what current ﬂows through the loop, and which way (left or right) does it pass through the resistor? b) If the current I in the solenoid is constnat but the solenoid is pulled out of the loop, turned around and reinserted, what total charge passes through the resistor? a) What is the current, which way does it ﬂow? Assume the solenoid is relatively long, only magnetic ﬁeld in loop is the B inside the solenoid, given by B = μ 0 nI . The ﬂux through the loop is then given by πa 2 B = πa 2 μ 0 nI . ε = - πa 2 μ 0 n dI dt . ε = IR I = 1 R πa 2 μ 0 nk. THe ﬂux due to the solenoid poinds to the right, and is increasing, so the current in the loop will ﬂow such that it produces a ﬂux inside the loop pointing left. b) What is the total charge in the change?

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## This document was uploaded on 09/28/2010.

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em14 - ELECTRICITY AND MAGNETISM I HOMEWORK 14: GRIFFITHS...

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