25: Charging a Conducting Rod

INTRO:

This problem explores the behavior of charge on conductors. We take as an example a long conducting rod suspended by insulating strings. Assume that the rod is initially electrically neutral. For convenience we will refer to the left end of the rod as end A, and the right end of the rod as end B. In the answer options for this problem, "strongly attracted/repelled" means "attracted/repelled with a force of magnitude similar to that which would exist between two charged balls.

Part A:
A small metal ball is given a negative charge, then brought near (i.e., within about 1/10 the length of the rod) to end A of the rod. What happens to end A of the rod when the ball approaches it closely this first time?

a) It is strongly repelled.
b) It is strongly attracted.
c) It is weakly attracted.
d) It is weakly repelled.
e) It is neither attracted nor repelled.

SOLUTION:
It is stated that the ball is much closer to the end of the rod than the length of the rod. Therefore, if points down the rod several times the distance of approach (but still much closer to end A than end B) are to experience no electric field, the charge on end A of the rod must be comparable in magnitude to the charge on the ball (so that their fields will cancel).

If you can recall the problem from this section, A Test Charge Determines Charge on Insulating and Conducting Balls, and the points made regarding conductors, it can be ascertained that in conductors, the electrons are free to move about. This means that when a charge is brought near to a conductor, the opposite charges all navigate to the point closest the charge and a strong attraction is created
this is true for a conducting rod as well, so the correct answer is option b)

NOTE:
Now consider what happens when the small metal ball is repeatedly given a negative charge and then brought into contact with end A of the rod.

Part B:
After a great many contacts with the charged ball, how is the charge on the rod arranged (when the charged ball is far away)?

a) There is positive charge on end B and negative charge on end A.
b) There is negative charge spread evenly on both ends.
c) There is negative charge on end A with end B remaining neutral.
d) There is positive charge on end A with end B remaining neutral.

SOLUTION: 
in a conductor, no matter how many times it comes in contact with a charge, if it returns to a static situation the charge returns to being neutral. This is satisfied by option b)

Part C:
How does end A of the rod react when the charged ball approaches it after a great many previous contacts with end A? Assume that the phrase "a great many" means that the total charge on the rod dominates any charge movement induced by the near presence of the charged ball.

a) It is strongly repelled.
b) It is strongly attracted.
c) It is weakly attracted.
d) It is weakly repelled.
e) It is neither attracted nor repelled.

SOLUTION:

The answer is a) 
but I can't exactly explain why
I am rather confused from this one 

Part D:
How does end B of the rod react when the charged ball approaches it after a great many previous contacts with end A?

a) It is strongly repelled.
b) It is strongly attracted.
c) It is weakly attracted.
d) It is weakly repelled.
e) It is neither attracted nor repelled.

SOLUTION:
Because the rod is a conductor, the charge is free to distribute itself over the entire rod. It must be distributed so that the internal electric field in the rod is zero, and there is only one distribution that achieves this. There is no memory in this situation: The charge will always distribute itself into the same final result. The rod is symmetric. Therefore, the final distribution of charge must also be symmetric, and hence the same charge must be on end A as on end B.
so the answer is a)