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University of TexasPHY 303Kmidterm 03-solutions

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This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A wire loop of radius R carrying a counterclockwise (wh ...

This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A wire loop of radius R carrying a counterclockwise (when viewed from the right) current I is moving to the right along the x-axis at a speed v. It passes around a second, stationary wire loop of radius a where a R. Choose the plot that correctly displays the qualitative behavior of the induced current I(t) in the stationary loop. On the plots, the +I axis represents clockwise current, while the −I axis represents counter-clockwise current (when viewed from the right on the +xaxis). 1. VIII: 2. I: correct 3. V: 4. II: 5. IV: 6. VI: 7. III:Version 085 – midterm 03 – chiu – (56565) 2 8. VII: Explanation: I is the correct choice. Before the current loop passes the wire ring, the flux through the ring points to the right and is increasing; to resist this change in flux, a clockwise (positive) current is induced in the ring. After the loop passes the ring, the flux still points to the right but is decreasing, inducing a counter-clockwise (negative) current in the ring. To get a sense of the functional form of the change in flux, note that we are entitled to use Bloop ∝ 1 (x2 + R2)3/2 since a R. (Since we are only interested in the qualitative behavior, we can leave off the constant factors and concern ourselves only with proportionality.) Since the area of the ring is not changing, dΦB/dt = Aring dBloop/dt. Again ignoring the constant factor Aloop, we calculate dBloop/dt, dBloop dt ∝ d dt (x2 +1R2)3/2 dBloop dt ∝ − 3 2 2x (x2 + R2)5/2 dx dt dBloop dt ∝ − 3xv (x2 + R2)5/2 Examining this result, we see that the presence of x in the numerator means our plot must pass through 0, while to either side of t = 0 we should expect some polynomiallike behavior. Combined with what we know about the sign of the current for times t < 0 and t > 0, I is the only correct option. 002 10.0 points A very long thick wire of radius R carries a current I, as in the following figure. I1 R Find the magnitude of the magnetic field inside the wire, a distance r from the center of the wire, where r < R. Assume current density is the same at every point inside the wire

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