Multiple-Choice Homework Problem 16.9 A positive point charge with charge +Q is

Question

Multiple-Choice Homework Problem 16.9 A positive point charge with charge +Q is placed and held inside a cavity in a neutral conductor as drawn. No charge is transferred to the conductor as the point charge is placed. Once the point charge is in place, the conductor is grounded. What is the total charge on the outer surface of the conductor after grounding? conductor +Q Select One of the Following: (a) 0 (b) +Q (c) ?Q (d) +Q/2 (e) ?Q/2

Multiple-Choice Homework Problem 16.10 The figure to the right shows a particle with positive charge, +Q, and three points around the particle. Both points 1 and 2 are a distance d from the particle and point 3 is a distance 2d from the particle. Rank the potential differences between the three points where ?Vij is the potential difference between point i and point j. If point i is at higher potential than point j, this quantitiy will be negative. Select One of the Following: (a) ?V13 = ?V23 = ?V12 (b) ?V13 < ?V23 < ?V12 (c) ?V13 > ?V23 > ?V12 (d) ?V13 = ?V23 < ?V12 (e) ?V13 = ?V23 > ?V12

Explanation / Answer

since is residing on the inner cavity,

net charge on the outer surface is Zero

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potential Differece V = KQ/d

so here,

1 and 3 are separated by r13^2 = d^2 + (2d)^2   

r13 = sqrt(5)*d

same is for r23 = sqrt(5)* d

V13 = V23 = (KQ/(sqrt5) * d)

1and 2 are separated by 2d so V12 = KQ/2d

so V13 = V23 < V12 ( option D)

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