- #1

rbrayana123

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## Homework Statement

http://oi50.tinypic.com/4i35g.jpg

I remember learning about this in Chemistry but boy I did not expect to actually prove it works haha. I've actually solved the problem but I feel a little uncomfortable with certain aspects.

## Homework Equations

E = [itex]\Delta[/itex]Vq

For uniform circular motion:

a = v^2/r

For two concentric cylinders with equal but opposite charge, the potential difference can be calculated out via Gaussian surface to be:

2kQ/L * ln(b/a) where L is the length of the cylinder.

## The Attempt at a Solution

First, I checked the potential difference and found it to be 2V * ln(b/a) which immediately tells me a lot about the system. Therefore, kQ/L = V (units seem to work out).

Conservation of Energy:

Vq = 0.5mv^2 --> v^2 = 2Vq/m

Using Gaussian surfaces, E(r) = 2kQ/Lr = 2V/r.

F(r) = E(r)q = 2Vq/r

a(r) = 2Vq/mr = v^2/r which is the equation of motion for uniform circular motion of radius r.

What's bothering me is that the reason I was able to solve this problem is because I'm *very* familiar with the coaxial cable conductor and quickly recognized it.

Provided the inner and the outer conductor did not have equal but opposite charges, would the potential still be the same or would it somehow be different? I think I solved this problem operating under the assumption they do but is it necessary to make that assumption?

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