have four identical conducting spheres: A, B, C, and D. In each scenario below,

Question

have four identical conducting spheres: A, B, C, and D. In each scenario below, sphere A starts with charge of +Q, while B, C, and D start out with no net charge, and then the spheres are touched to each other and separated in the order described. Any spheres not in contact are held very far away. For each scenario, give the final charge of sphere B as a whole number fraction of Q. For example, if you decide that the final charge of sphere B is Q/7, enter "1" in the numerator and "7" in the denominator. Remember! Before each scenario begins, spheres A, B, C, and D are reset to charges of +Q, 0, 0, and 0 again. Scenario 1: A and B touch and are separated, then A and C touch and are separated, then A and D touch and are separated. Q_B = times Q Scenario 2: A and B touch and are separated, then B and C touch and are separated, then C and D touch and are separated. Q_B = times Q Scenario 3: A and D touch and are separated, then D and C touch and are separated, then D and A touch and are separated, then A and B touch and are separated. Q_B = times Q

Explanation / Answer

When charges are touched , charge on them becomes the average

For the first case

Qb = (Q+ 0 )/2 = Q/2

for the second case

when A and B are touched

Qb = Q + 0/2 = Q/2

when B and C are touched

Qb = (Q/2 + 0 ) /2 = Q/4

so Qb = Q/4

For the third case

A and D are touched

QA = Qd = (Q + 0) /2 = Q/2

now D and C are touched

Qd = Qc = (Q/2 + 0 ) / 2= Q/4

D and A are now touched

Qd = Qa = (Q/2 + Q/4 ) = 3Q/8

now A and B are touched

Qa = Qb = (3Q/8 + 0 )/ 2 = 3Q/16

Qb = 3Q/16

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