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#1 2008-02-10 21:05:55

gathan77
New Member
Registered: 2008-02-10
Posts: 1

Potential Difference Question

This was a recent problem on an exam that I did poorly on that I was wondering if I could acquire some assistance on to further my understanding.

A long plastic pipe has an inner radius A and an outer radius B. Charge is uniformly distributed over the volume A<r<B, and the amount of charge is \rho C/m^{3}. Find the potential difference between r=B and r=0.

I'm stumped on how to carry out this problem, but I'm thinking that using Gauss's Law to find the electric field would be helpful so that you can then integrate it to find V. However, my triple integral skills are a little shaky and I'm not sure if this is the the correct way. Any help would be appreciated. Thanks

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#2 2008-02-11 05:42:47

Martin
Moderator
From: Earth
Registered: 2004-10-04
Posts: 380

Re: Potential Difference Question

gathan77 wrote:

This was a recent problem on an exam that I did poorly on that I was wondering if I could acquire some assistance on to further my understanding.

A long plastic pipe has an inner radius A and an outer radius B. Charge is uniformly distributed over the volume A<r<B, and the amount of charge is LaTeX Image. Find the potential difference between r=B and r=0.

I'm stumped on how to carry out this problem, but I'm thinking that using Gauss's Law to find the electric field would be helpful so that you can then integrate it to find V. However, my triple integral skills are a little shaky and I'm not sure if this is the the correct way. Any help would be appreciated. Thanks

Your approach is correct. As far as being concerned about triple integration, you need to realize that the geometry has significant symmetry. Ultimately, you will find that the electric field depends only upon the radius r, and the potential difference will involve integration over the single variable r.


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