Midterm - Version 027/AABCD midterm 01 Turner (59130) 1...

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Unformatted text preview: Version 027/AABCD midterm 01 Turner (59130) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Four charges are fixed at the corners of a square centered at the origin as follows: q at ( a, + a ); 2 q at (+ a, + a ); 3 q at (+ a, a ); and 6 q at ( a, a ). A fifth charge + q with mass m is placed at the origin and released from rest. Find the speed when it is a great distance from the origin, where the potential energy of the fifth charge due to the four point charges is negligible. 1. bardbl vectorv bardbl = q radicalBigg 2 2 k ma 2. bardbl vectorv bardbl = q radicalBigg 6 6 k ma 3. bardbl vectorv bardbl = q radicalBigg 2 5 k ma 4. bardbl vectorv bardbl = q radicalBigg 3 3 k ma 5. bardbl vectorv bardbl = q radicalBigg 6 3 k ma 6. bardbl vectorv bardbl = q radicalBigg 3 6 k ma 7. bardbl vectorv bardbl = q radicalBigg 6 2 k ma correct 8. bardbl vectorv bardbl = q radicalBigg 3 5 k ma 9. bardbl vectorv bardbl = q radicalBigg 3 2 k ma 10. bardbl vectorv bardbl = q radicalBigg 6 5 k ma Explanation: x a +6 q a 3 q +2 q + q + q, m 2 a The initial energy of the charge is E i = K i + U i = U i = q parenleftbigg k q 2 a + 2 k q 2 a + ( 3 q ) k 2 a + 6 k q 2 a parenrightbigg = 6 k q 2 2 a . The final energy is E f = 1 2 mv 2 . From energy conversation, we have E i = E f 6 k q 2 2 a = 1 2 mv 2 v = q radicalBigg 6 2 k ma . 002 10.0 points Consider a conducting sphere with radius R and charge + Q, and a conducting spherical shell with inner radius 2 R , outer radius 3 R and net charge + Q. + Q + Q 3 R radius 2 R radius R radius Select the electric field vs radial distance diagram [ E ( r ) function] which describes this situation. Version 027/AABCD midterm 01 Turner (59130) 2 1. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 r R 2 R 3 R E parenleftbigg kQ 18 R 2 parenrightbigg 2. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 r R 2 R 3 R E parenleftbigg kQ 18 R 2 parenrightbigg 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 r R 2 R 3 R E parenleftbigg kQ 18 R 2 parenrightbigg cor- rect 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 r R 2 R 3 R E parenleftbigg kQ 18 R 2 parenrightbigg 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 r R 2 R 3 R E parenleftbigg kQ 18 R 2 parenrightbigg Explanation: The charge on the inner sphere is + Q. The net charge on the spherical shell is the sum of the charges on its surfaces + Q. The charge on the inner surface of the spherical shell is the opposite sign of the charge on the inner sphere Q....
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Midterm - Version 027/AABCD midterm 01 Turner (59130) 1...

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