Question

You have four identical conducting spheres: A, B, C, and D. In each scenario below, sphere A starts with a charge of -Q, sphere C starts out with a charge of +Q, and spheres B and D start out neutral. 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 A as a whole number fraction of Q For example, if you decide that the final charge of sphere A 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, +Q, 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 D 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

Answer 1

here A is - Q , B is 0, C is +Q   and D is 0

so

Scenario 1 :

A and B when touched , net = -Q+0 = -Q

A and C when touched, Net = -Q+Q = 0

A and D when touched , Net = -Q +0 = -Q

Net charge in Scenario 1   = -Q+0-Q = - 2Q

Scenario 2:

A and B when touched , net = -Q+0 = -Q

B and D when touched, Net = 0+0 = 0

C and D when touched , Net = Q +0 = +Q

Net charge in Scenario 2   = -Q+0+Q = 0 Q

Scenario 3 :

A and D when touched, net = -Q+0 = -Q

D and C when touched, Net = 0 +Q = +Q

D and A when touched , Net = +Q -Q   = 0

A and B when touched , net = -Q +0 = -Q

Net charge in Scenario 3   = -Q+Q+0-Q = - 1Q