# Charge Equality Between Different Size Pith Balls

• slickvic
In summary, when identical pith balls come in contact to make q1=q2, the charges would be equal if the balls were of different size. Putting the balls in contact forces their potential to be the same, and separating them would result in the smaller ball containing less charge. Connecting them with a wire would also equalize their potential, with the ratio of charges being equal to the ratio of the radii. This holds true for metal balls, and may also be applicable to disks or straight rods. However, further analysis is needed to determine the exact ratio for these shapes.

#### slickvic

Suppose you let identical pith balls come in contact to make q1=q2. Would the charges be equal if the pith balls were of different size?

You know, I vaguely remember doing this problem way back in freshman physics. Just a guess on my part, but I think that putting the balls in contact would make the charge density uniform. If my assumption is correct, then when you separate the balls, the smaller one would contain less charge.

I'm not real sure about pith, but I can answer for metal balls...

Putting the balls in contact forces their potential to be the same. The problem is easier if the balls are separated by a distance large compared to their size. Briefly connecting them with a wire would force the potential at each ball to be the same. In this case the ratio of charges would be equal to the ratio of the radii.

mdelisio said:
I'm not real sure about pith, but I can answer for metal balls...

Putting the balls in contact forces their potential to be the same. The problem is easier if the balls are separated by a distance large compared to their size. Briefly connecting them with a wire would force the potential at each ball to be the same. In this case the ratio of charges would be equal to the ratio of the radii.

Are you sure it wouldn't be equal to the ratio of the cube of their radii?

I'm asking because I'm also considering lesser dimensional problems. What if, instead of spheres, we were talking about disks, or straight rods? Well, maybe I should work the problem for myself and get back to you guys.