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practice_key_v2 - Prelim2 Practice Answer Key 1 true or...

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Prelim2 Practice Answer Key 1. true or false F, it has to be vector sum. F, Gauss’ Law gives the net electric field. F, think about an electron moving inside a capacitor with initial velocity perpendicular to the ~ E field. F, the flux remains constant. T F, the electric potential is constant but not necessarily zero. F, the charges are on the inner surfaces. F, with the voltage unchanged and the capacitance decreased, the total charge decreases. F, the battery near the end of its useful life has the same emf, but a much larger internal resistance. F, the parallel case has larger power. T F, only true if the electric field is uniform. T 2. C, the two spheres will be at equal potential if connected by a wire. 3. C, 4. C, A, C 5. C, C, B, A (the capacitor has to do work so that the energy stored in it will decrease.) 6. see graphs at the end 7. (a) Inner: -Q, Outer: +2Q, (b) The electric field E ( r ) = Q 2 π 0 r 2 , r > 3 R E ( r ) = Q 4 π 0 r 2 , R < r < 2 R (c) and (d), see graphs at the end (e) take V ( ) = 0 by convention, V (2 R ) = V (3 R ) = Q 6 π 0 R V ( R ) = V (2 R ) + Z 2 R R E ( r ) dr = 7 Q 24 π 0 R 1
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(f) E ( r ) = Q r 4 π 0 R 3 , for 0
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