Only one of three balls A, B, and C carries a net charge q. The balls are made from conducting material and are identical. One of the uncharged balls can become charged by touching it to the charged ball and then separating the two. This process of touching one ball to another and then separating the two balls can be repeated over and over again, with the result that the three balls can take on a variety of charges. Which one of the following distributions of charges could not possibly be achieved in this fashion, even if the process were repeated a large number of times?
a. qA = 1/3q, qB = 1/3q, qC = 1/3q
b. qA = 1/2q, qB = 1/4q, qC = 1/4q
c. qA = 1/2q, qB = 3/8q, qC = 1/4q
d. qA = 3/8q, qB = 3/8q, qC = 1/4q.

When a charged object is brought into contact with an uncharged conducting object, the charge flows from the body at higher potential (charged object) to the body at lower potential (uncharged object). However, the total charge in this process remains the same i.e. total charge of both the objects after they are brought into contact must be equal to the total charge before they were brought into contact.

We are given three balls: A, B and C. Only one of these balls carry a net charge that is equal to q. The other two balls are neutral. So the total charge before these balls are brought into contact is q.

After they are brought into contact the total charge must still be the same. So, for the given options we calculate the total charge. Any amount of charge greater than or less than q would not be the possible scenario and cannot be achieved.

Option A:

qA + qB + qC = [tex]\frac{1}{3}q+ \frac{1}{3}q+\frac{1}{3}q=q[/tex]

Hence, this distribution is possible as the total charge stays the same.

Option B:

qA + qB + qC = [tex]\frac{1}{2}q+ \frac{1}{4}q+\frac{1}{4}q=q[/tex]

Hence, this distribution is possible as the total charge stays the same.

Option C:

qA + qB + qC = [tex]\frac{1}{2}q+ \frac{3}{8}q+\frac{1}{4}q=\frac{9}{8}q[/tex]

The total charge is greater than q, which is not possible. So this distribution of charges is not possible and cannot be achieved even if the process were repeated a large number of times.

Option D:

qA + qB + qC = [tex]\frac{3}{8}q+ \frac{3}{8}q+\frac{1}{4}q=q[/tex]

Hence, this distribution is possible as the total charge stays the same.

Therefore, the answer to this question is option c. qA = 1/2q, qB = 3/8q, qC = 1/4q