Potential difference of concentric conducting shells

[faint545]

Two concentric conducting spherical shells have equal and opposite charges. The inner shell has outer radius $a$ and charge $+q$; the outer shell has inner radius $b$ and charge $-q$. Find the potential difference $V_{a}-V_{b}$ between the shells

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?

 

[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.

 

[faint545]

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.

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?

 

[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?

 

[faint545]

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?

Alright... see attached image.

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

 

[G01]

Alright... see attached image.

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

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.

 

[faint545]

thanks for your guidance

 

[G01]

thanks for your guidance

No problem!