Capacitance in concentric shells

  • Thread starter OptimusPwn
  • Start date
  • #1

Homework Statement



Consider four concentric spherical metal
shells of radii r, 2r, 3r, and 4r. The middle
two shells are connected by wire, as shown.
What is the total capacitance of the system?
In your solution, clearly explain your method.

Homework Equations



u= 1/2cv^2

The Attempt at a Solution


So my teacher told us to assume we can hook it up to a battery(voltage) and that the two inner shells have the same charge and to evaluate the potential inner to outer, but I have no idea how to do this.
 

Answers and Replies

  • #2
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,797
1,382
There's a number of details you'll have to figure out for yourself, but here's generally how to approach the problem. Assume there is a charge +Q on the inner sphere. Use Gauss's law to calculate the electric field between the spheres. You'll have to figure out what the charge of the other spheres as well. Once you know the electric field, you can integrate it to calculate the potential difference between the spheres.
 
  • #3
So when I do that I get

E(r)= Q/4(pi)(R)2Epilsonknot


E(2r)=Q/4(pi)(2R)2Epilsonknot


E(3r)=Q/4(pi)(3R)2Epilsonknot

E(4r)=Q/4(pi)(4R)2Epilsonknot


Then I use V=Ed so I integrate this?

What am I integrating though, the difference between the electric fields or the distance?
I am stuck beyond this point and are my electric fields right?
 
  • #4
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,797
1,382
I think you need to go back and review how the electric field and potential difference are related (beyond just plucking formulas out of the book) and then reread my previous post.

Your electric fields are not correct. You want the electric field for the regions between the spheres. Also, you can't use V=Ed here.
 

Related Threads on Capacitance in concentric shells

  • Last Post
Replies
2
Views
2K
Replies
2
Views
4K
Replies
1
Views
2K
Replies
5
Views
6K
Replies
6
Views
23K
  • Last Post
Replies
1
Views
3K
Replies
6
Views
5K
  • Last Post
3
Replies
64
Views
6K
Replies
82
Views
11K
Replies
1
Views
7K
Top