• Support PF! Buy your school textbooks, materials and every day products Here!

Electric Potential of a Spherical Shell of Charge

  • Thread starter Polarbear
  • Start date
  • #1
3
0
Ok if you have a spherical shell of radius R with an even distribution of charge then outside the shell at a distance r where r>R I get that the shell can be treated as a point charge and inside the sphere (r<R) the electric potential will be constant.
All my notes cover when the shell has no thickness and I was thinking what happen if the spherical shell did have thickness (say inner radius a and outer radius b)? When r is greater then b can the shell still be treated as a point charge? How about when a<r<b?
 

Answers and Replies

  • #2
Doc Al
Mentor
44,874
1,122
If the charge is uniformly distributed throughout the (nonconducting) shell:

(r > b) Treat as a point charge

(r < a) potential will be constant

(a < r < b) the field (and potential) will vary throughout this range; you'll need to integrate. (The field at a radius r depends only on the charge within that radius; the field is that of a point charge, but only the charge within r contributes to the field.)
 
  • #3
3
0
Thanks for just clearing that up for me. I've managed to find a question on this (I'm getting practise in before mid-year exams) however it deals in terms of charge density. Is it just as simple as finding Q in terms of the sphere (volume of shell at such and such density).
 
  • #4
Doc Al
Mentor
44,874
1,122
Right. You should be able to work with either total charge Q or with the charge density. As an exercise, you might want to find the field as a function of radius for a uniform ball of charge density [itex]\rho[/itex].
 

Related Threads for: Electric Potential of a Spherical Shell of Charge

Replies
5
Views
425
Replies
6
Views
3K
Replies
11
Views
481
Replies
3
Views
14K
Replies
3
Views
1K
Replies
16
Views
7K
Top