Question

u 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. 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 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 3

Answer 1

Scenario 1 –

A and B touch and are separated. Then B does not touch any of the rest sphere.

So, charge on B, Q(B) = Q / 2

Scenario 2 –

A and B touch.

So, charge on B = Q/2

Again, B and C touch.

Then the resulting charge on B = (1/2)*(Q/2) = Q/4

Scenario 3 –

A and D touch each other.

So, Q(A) = Q(D) = Q/2

Again, D and C touch each other.

So, Q(D) = Q(C) = (1/2)*Q/2 = Q/4

Then D and A touch each other.

So, Q(D) = Q(A) = (1/2)*(Q/2 + Q/4) = (3/8)Q

Then, A and B touch each other.

So, Q(A) = Q(B) = (1/2)* (3/8)Q = (3/16)Q

Therefore, the resulting charge on B, Q(B) = (3/16)Q