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Seung · 2008-03-19 03:04:07

Having trouble solving one problem for homework and none of my friends seemed to get the right answer.

The question is:

"A +30-µC charge is placed 32 cm from an identical +30-µC charge. How much work would be required to move a +0.50-µC test charge from a point midway between them to a point 10 cm closer to either of the charges?"

The answer I got was like: $3.2 x 10^{10}$ by using the equation:

$W = q (\frac{kQ}{r_{b}} - \frac{kQ}{r_{a}})$ .

The answer in the back of the book was: 1.08J.

Any help is deeply appreciated and thanks in advance.

--Seung

Last edited by Seung (2008-03-20 03:33:55)

Chris · 2008-03-19 20:49:58

I have no idea what this problem is talking about!

from a point midway between them to a point 0 cm closer to either of the charges?

If you move the test charge 0 cm closer to either, then you haven't moved the test charge at all. The answer would be zero.

If they mean that you move the test charge within 0 cm of one of the charges then the difference in potential would be infinite!

Seung · 2008-03-20 03:32:57

I am so, so sorry. I meant to say that the test charge would move to a point 10 cm closer to either of them. I should have looked over my post for any errors. >.< I believe I fixed it above.

EDIT: Also, thank you Chris for pointing it out. ^-^

Last edited by Seung (2008-03-20 03:47:09)

Chris · 2008-03-20 17:44:18

That makes much more sense!

I get the same answer as the back of your book: 1.08 J.

Instead of jumping straight to the work, think about the difference in potential energy between the two points. Determine the electric potential at the first point:

$V_1 = kQ\frac{1}{r} + kQ\frac{1}{r} = 2kQ\frac{1}{r}$

where Q is the charge of the large charges. The electric potential for some point displaced by some value d is:

$V_2 = kQ\frac{1}{r-d} + kQ\frac{1}{r+d} = kQ[\frac{1}{r-d} + \frac{1}{r+d}]$

The difference in potential $\Delta V$ is just $V_2 - V_1$ . The work will just be this value times the test charge.

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#1 2008-03-19 03:04:07

Electric Potential Due to Point Charges

#2 2008-03-19 20:49:58

Re: Electric Potential Due to Point Charges

#3 2008-03-20 03:32:57

Re: Electric Potential Due to Point Charges

#4 2008-03-20 17:44:18

Re: Electric Potential Due to Point Charges

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