- #1

Black Armadillo

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## Homework Statement

A ring of diameter 7.10 cm is fixed in place and carries a charge of 5.00 μC uniformly spread over its circumference. How much work does it take to move a tiny 3.40 μC charged ball of mass 1.70 g from very far away to the center of the ring?

## Homework Equations

I tried using: [tex]W=-\Delta U[/tex]

## The Attempt at a Solution

We know that when the ball is very far away U=0J

Then to find the potential energy when the ball is in the center of the ring I did:

Change in charge is [tex]5.00X10^{-9}C/2\pi(0.0710m)=1.12X10^{-8}C/m[/tex]

[tex]\int \frac{k*q*dq}{r} ds[/tex] from 0 to 2pi.

[tex]\frac{k*q*dq}{r} \int ds[/tex] from 0 to 2pi.

[tex]\frac{8.988X10^{9}N*m^2/C^2*3.40X10^{-9}C*1.12*10^{-8}C/m}{0.0710m} \int ds[/tex] from 0 to 2pi [tex]=3.031X10^-5J[/tex].

[tex]W=-\Delta U=-(3.031X10^-5J-0J)=-3.031X10^-5J[/tex]