Homework Help: Potential difference of concentric conducting shells

1. Sep 27, 2011

faint545

My professor said to in order to solve this, integrate the electric field to find the electric potential...

$\Delta V = -\int\stackrel{\rightarrow}{E}dl$

My question is, using Gauss's Law, ($\oint E_{n}dA = \frac{Q}{\epsilon}$), how do I go about finding Q?

Isn't Q just the charge of the shell?

2. Sep 27, 2011

G01

In Gauss's law, Q is the charge enclosed by your Gaussian surface. So, first decide where you Gaussian surface will be, then add up all the charge inside of it.

HINT: You want your surface to be in the region where you want to find the electric field.

3. Sep 27, 2011

faint545

This is what I have drawn (see attachment). Is the basic idea here to integrate the electric field of the outer Gaussian surface from b to a? If so, what about the inner Gaussian surface?

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• 2011-09-27_20-21-30_086.jpg
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4. Sep 28, 2011

G01

You want to find the potential difference between the shells, so you don't need the Gaussian surface outside the larger shell.

Try this: Take your inner surface and place it at an arbitrary point r. Then, find E using the standard approach when using Gauss's law. You will then have E between the plates as a function of r. Can you use that to find the potential difference between the plates?

5. Sep 28, 2011

faint545

Alright... see attached image.

Now, how do i determine if i should integrate from a to b or from b to a?

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• 2011-09-28_12-25-07_614.jpg
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6. Sep 28, 2011

G01

That all looks good.

As far as your integration bounds are concerned, it doesn't matter. The sign of your end result will change, but that's just like hooking up a voltmeter in reverse: You will still get the right pot. difference, just the sign will change.

7. Sep 29, 2011

faint545

thanks for your guidance

8. Sep 29, 2011

G01

No problem!

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