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312ps2 - PROBLEM SET 2 ECE 312 Autumn Quarter 2010 Assigned...

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PROBLEM SET 2 ECE 312 Autumn Quarter 2010 Assigned: October 1st Due: October 8th in class Instructor: Joel Johnson Problem 1 A single loop of wire of radius b is centered on the z axis in a cylindrical coordinate system. Assume that a voltage source V t ( ) is connected to this loop through a resistance R ; when V t ( ) is constant in time, a current φ ˆ I t ( ) flows in the loop. This current produces a magnetic flux density B z ˆ μ 0 I t ( ) 2 b -------------- = inside the area bounded by the loop, where t indicates time in seconds. (Note this is only an approximation of the true magnetic flux density that would result from use of the Biot- Savart law.) Now assume that V t ( ) is no longer constant in time. z b φ ˆ I t ( ) R + - V 1 2 (a) Find the magnetic flux linking the loop. (b) Calculate the EMF induced in the loop by Faraday’s law. (c) Comparing your part (b) answer with circuit theory concepts, what is the approximate inductance of this wire? Discuss any sign changes you need to make. Note this is approximate because our original magnetic flux density was approximate.
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