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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