PHYSICS 240 Exam 3 -- Fall 2003 Solutions

PHYSICS 240 Exam 3 -- Fall 2003 Solutions - Physics 240...

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Physics 240 Fall 2003: Exam #3 Solutions Please print your name:___________________________________________________ Please list your discussion section number:___________________________________ Please list your discussion instructor:________________________________________ Form #1 Instructions 1. Fill in your name above 2. This will be a 1.5 hour, closed book exam. The exam includes 20 questions. 3. You may use a calculator, please do not share calculators 4. You may use three 3”x5” note cards (two from the earlier exams, plus one new one) with notes and equations you think may be useful. You can write on both sides of the card if you like. 5. You will be asked to show your University student ID card when you turn in your exam. ID checked by:___________________________________ Table of constants: ε 0 = 8.85 x 10 -12 C 2 /Nm 2 k = 1/(4 πε 0 ) q electron =-1.6 x 10 -19 C q proton =1.6 x 10 -19 C m electron =9.1 x 10 -31 kg m proton =1.67 x 10 -27 kg µ 0 = 4 π x 10 -7 Tm/A G = 6.67 x 10 -11 Nm 2 /kg 2
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from zero at the center of the wire to some value j edge at the outer edge. Such a current density can be expressed j(r) = (j edge /R)r. What is the magnetic field inside the wire, at a distance “a” from the center of the wire? A) * µ 0 j edge a 2 / 3R B) µ 0 j edge a / 2R C) 2 πµ 0 j edge / R D) 2 πµ 0 j edge a E) 2 µ 0 j edge a 2 / R 2: A small bar magnet is dropped, north pole down, towards the centers of several different loops of wire, each of which is held fixed in place. Loop A has resistance R, loop B has resistance 2R, and loop C has a small break in it. Which of the following statements is correct? A) The magnet accelerates downward at the same rate in each case B) The magnet accelerates down toward loop C, but accelerates up and away from loops A and B C) The magnet accelerates down towards all loops, most rapidly towards, B, most slowly towards C D) The magnet accelerates down towards all loops, most rapidly towards A, most slowly towards B E) *The magnet accelerates down towards all loops, most rapidly towards C, most slowly towards A S N C S N B S N A This problem, in essentially this form, was a problem you did in your discussion sections. To solve it, use Ampere’s Law: B dl = µ 0 I inside Taking a circle at a position r, we have B*2 π r = µ 0 2 π j(r)rdr = 2 πµ 0 (j edge /R) r 2 dr = (2/3) πµ 0 (j edge /R)r 3 Solving for B we find: B = µ 0 (j edge /3R)r 2 And evaluating at r=a, we have B = µ 0 j edge a 2 /3R In each case, the falling magnet will induce an EMF in the loop, and in each case that EMF will be the same. This EMF will induce a different current in each loop. In loop C (with effectively infinite resistance) this current will be zero. In loop B, with resistance 2R, it will be I B , and in loop A, with resistance R, it will be I A = 2I B . These induced currents will present magnetic fields which oppose the fall of the magnet. When the induced current is
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This test prep was uploaded on 04/01/2008 for the course PHYSICS 240 taught by Professor Davewinn during the Fall '08 term at University of Michigan.

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PHYSICS 240 Exam 3 -- Fall 2003 Solutions - Physics 240...

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