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 C as a whole number fraction of Q. For example, if you decide that the final charge of sphere C 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 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.
Scenario 3: A and B touch and are separated, then B and D touch and are separated, then C and D touch and are separated.

Answer 1

Answer:

1)    Q_c = - ½ Q ,  2)   Q_c = + ¼ Q , 3)    Q_c= 3/8 Q

Explanation:

For this exercise we must use that equal charges repel and charges with different signs attract. When two objects are in contact, the charges are evenly distributed between them.

Scenario 1.

when the two spheres touch the charge -Q is distributed between them, when separating each sphere has a charge = -1/2 Q

as there are no more interacts sphere C its charge is

         Q_c = - ½ Q

Scenario 2

when the two spheres touch the charge -Q is distributed between them, when separating each one has a charge

        Q_a = Q_d = - ½ Q

now the sphere D and C touch the charge is Q_net = -1/2 Q + Q = + ½ Q

when separating each sphere has half the charge

            Q_d = Q_c = + ¼ Q

since sphere C has no more interaction, its charge is

           Q_c = + ¼ Q

Scenario 3

A and B touch the net charge is Q_net = - Q + 0 = - Q

when parting

          Q_a = Q_b = - ½ Q

now B and D touch, the charge is Q_net = - ½ Q +0 = - ½ Q

when parting

           Q_b = Q_d = - ¼ Q

finally C and D touch

the net charge is Q_net = Q- ¼ Q = ¾ Q

when separating each one is left with half the load

           Q_c = Q_d = 3/8 Q

          Q_c= 3/8 Q