HW help, basic E+M for the physics kids.

[TheVrolok]

Two friends of mine call me up tonight to ask me this because you know, I took physics once. Oh wait, that was three years ago .. and even tho the MCAT jogged my memory last year, I've once again lost all my knowledge of E+M. Oh, it gets worse, my roomie, and EE major, can't remember either, so here it is 😛

So you have point C, lying in what would be the center of a circle that is composed simply of a half circle. Opposite this half circle is a point charge. The arc that is the half circle has the same amount of charge distributed over itself as exists in the point charge. Which, the half circle or the point charge, produces more force on the point C?

pic

both radii are the same distance. arc has charge Q evenly distributed, point on the right has -Q of equal magnitude. Which puts more force on the center point, C? (if either)

 

[DanFungus]

My thinking is that since the force is proportional to the charge and inversely proportional to the distance, sum up the charge on the half circle (this sum == total charge of the point charge). Each of these charges on the half circle are equidistant from point C, which is also equal to the distance from C to the point charge. The total (MAGNITUDE) of the force would be equal since you have the same net charge, and the same net distance.
However, point C would experience a force pulling or pushing towards the point charge because the point charge would be using it's entire charge in the horizontal dimension, whereas the half circle would be using some of the charge to pull up and down - canceling each other out - so it would still move horizontally, but there would be less net force to fight the force from the point charge.

 

[chuckywang]

You're gonna need to integrate to find the total force from the half circle. Use symmetry to cancel out some terms.