B. How does the ball's potential energy relate to the amount of work needed to place
the ball on the 2-m shelf?

the displacement produced by the body.  

the amount of force subjected to the body.  

the angle between the direction of force and displacement

the answer is f1 and d2 because if you put equal force on those two points the beam would balance trust me on this

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach