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I need help seeing if I did this right....

This is from Fundamentals of Physics, 8th edition, volume 2. By Jearl Walker.

Chapter 24, problem 88.

A particle of positive charge Q is fixed at point P. A second particle of mass m and negative charge -q moves at a constant speed in a circle of radius [tex]r_{1}[/tex] centered at P. Derive an expression for the work W that must be done by an external agent on the second particle to increase the radius of the circle of motion to [tex]r_{2}[/tex].

2. Relevant equations

[tex]

W_{\vec{E}} = -\int_{r_{1}}^{r_{2}} \vec{E}\cdot d\vec{r}

[/tex]

[tex]

\vec{E} = \frac{1}{4\pi\epsilon_{0}} \frac{Q}{r^2} \hat{r}

[/tex]

3. The attempt at a solution

Here's what I'm thinking. The work against the electric field is just the integral above. Since the particle stays on an equipotential surface, I should only have to worry about work outward, right?

Here's what I have:

[tex]

W_{total} = W_{\vec{E}} = \left(\frac{1}{r_{2}} - \frac{1}{r_{1}}\right) \left(\frac{Q}{4\pi\epsilon_{0}}\right)

[/tex]

Please help point out if I've done something wrong!

-Mike

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# Homework Help: Work against an electric field due to a point charge

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