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

Question

You have four identical conducting spheres: A, B, C, and D. In each scenario below, sphere A starts with a 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. enario 2: A and B touch and are separated, then B and C touch and are separated, then C and D touch and are separated. 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.

Explanation / Answer

1)Scenario 1 is correct that is if A&B are touch then charge on B is Q+0/2=1/2*Q

2)Scenario 2 is incorrect that is if A&B are touch then charge on B is Q+0/2=1/2*Q ,B&Care touch and seperated then

QB=Q/2+0/2=Q/4

3)scenario3 is correct if A&D are touch and seperated QA=Q/2,QD=Q/2

D&C are touch and seperated QD=Q/2,QC=Q/4,similarlyD&A thenQD=Q/4+Q/2/2=3Q/8,similarQA=3Q/8,

finallyA&Bthen QB=3Q/8+0/2=3Q/16

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