midterm 03-solutions

# midterm 03-solutions - Version 085 – midterm 03 – chiu...

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Unformatted text preview: Version 085 – midterm 03 – chiu – (56565) 1 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 counter- clockwise (when viewed from the right) cur- rent I is moving to the right along the x-axis at a speed v . It passes around a second, sta- tionary 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 cur- rent (when viewed from the right on the + x- axis). 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 increas- ing; to resist this change in flux, a clockwise (positive) current is induced in the ring. Af- ter the loop passes the ring, the flux still points to the right but is decreasing , induc- ing 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 B loop ∝ 1 ( x 2 + R 2 ) 3 / 2 since a ≪ R . (Since we are only inter- ested in the qualitative behavior, we can leave off the constant factors and concern our- selves only with proportionality.) Since the area of the ring is not changing, d Φ B /dt = A ring dB loop /dt . Again ignoring the constant factor A loop , we calculate dB loop /dt , dB loop dt ∝ d dt parenleftbigg 1 ( x 2 + R 2 ) 3 / 2 parenrightbigg dB loop dt ∝ − 3 2 2 x ( x 2 + R 2 ) 5 / 2 dx dt dB loop dt ∝ − 3 xv ( x 2 + R 2 ) 5 / 2 Examining this result, we see that the pres- ence of x in the numerator means our plot must pass through 0, while to either side of t = 0 we should expect some polynomial- like behavior. Combined with what we know about the sign of the current for times t < 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. I 1 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. 1. μ 2 π IR 2 r 3 2. μ 2 π IR r 2 3. μ 4 π Ir 2 R 3 4. μ 2 π Ir 2 R 5. μ 2 π Ir R 2 correct 6. μ 2 π Ir 2 R 3 7. μ 4 π IR r 2 8. μ 4 π Ir 2 R 9. μ 4 π Ir R 2 10. μ 4 π IR 2 r 3 Explanation: The current density (current/area) is the same throughout the wire. Sketch an Ampe- rian loop within the wire with radius r . Then, the current through this loop i divided by area of this loop is equal to the total current per unit area....
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## This note was uploaded on 02/21/2012 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas.

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midterm 03-solutions - Version 085 – midterm 03 – chiu...

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