When a conducting sphere is charged positively, initially the charge is deposited on the left side. However, due to the sphere's conducting nature, the charge spreads uniformly throughout the surface to the sphere. Charge is uniformly distributed because:

A. charged atoms at the location of charge distribute throughout the surface.
B. excess protons move from the location of charge to rest.
C. excess protons within the sphere move toward excess protons.
D. excess charge within the sphere moves out into the ground from the surface.

All answers are wrong. At least, if this were not multpile choice then, reasonably speaking, a teacher would have to mark any of the answers as "not correct".

The reason why the charge spreads out uniformly is because a non uniform charge distribution gives rise to a electric field.

The force on a charge is the charge times the electric field, so the charge will move. The charges will stop to move when the electric field is zero. This is the case when the charges are uniformly distributed.

I know, it's annoying.... I'm just putting A..

Answer A is wrong because it is not charged atoms that move. It is free electrons. The teacher should know better.

All the other answers are also wrong

To determine why the charge spreads uniformly throughout the surface of the conducting sphere, let's analyze each given statement:

A. Charged atoms at the location of charge distribute throughout the surface.
This statement is incorrect because there are no charged atoms involved in the process. Instead, we are dealing with excess charge, specifically excess protons.

B. Excess protons move from the location of charge to rest.
This statement is also incorrect. Excess protons do not "move to rest" – rather, they redistribute themselves across the surface of the sphere.

C. Excess protons within the sphere move toward excess protons.
This statement is false as well. Excess protons within the sphere are not attracted to other excess protons. Instead, they move around and redistribute themselves across the surface of the sphere.

D. Excess charge within the sphere moves out into the ground from the surface.
This statement is incorrect. The excess charge within the sphere does not move out into the ground. Instead, it redistributes itself on the surface of the sphere.

The correct answer is actually none of the provided options. The charge spreads uniformly throughout the surface of the conducting sphere because of the principle called electrostatic repulsion. Excess protons repel each other due to their like charges. As a result, they evenly distribute themselves on the surface of the sphere to minimize their mutual repulsion, leading to a uniform charge distribution.