Spherical Capacitor: Solving Electric Field, Displacement Field & Capacitance

In summary, the conversation is about solving a problem involving a spherical capacitor with two dielectrics and charges of +q and -q on the inner and outer surfaces. The solution involves finding the electric and displacement fields in each region, calculating the capacitance of the capacitor, and determining the surface charge on one of the dielectrics at a specific radius. The solution for part c) involves using Gauss's Law to find the charge on the dielectric. The person asks for a nudge in the right direction and thanks the other person for pointing out the solution.
  • #1
discoverer02
138
1
I'm stuck on the last part of the following problem:

A spherical capacitor has inner radius R and outer radius 3R, and contains to dielectrics, of permittivities e1, which extends from R to 2R, and e2, which extends from 2R to 3R. Assume charges of +q and -q on the inner and outer surfaces.

a) find E (electric field) and D (displacement field) in each region as functions of r.

b) find the capacitance of the capacitor.

c) what is the surface charge on the e1 dielectric at radius R?

for part a) D = (Einitial)(e) = (kq/r^2)e = q/(4pir^2) for both regions.

and E1 = D/e1 = q/(4e1pir^2)
E2 = D/e2 = q/(4e2pir^2)

for part b) V1 = q/(4piRe1) and V2 = Q(24piRe2)

so C1 = 4piRe1 and C2 = 24piRe2 and Ctotal = 24piRe1e2/(6e2-e1)

Having found all this I don't quite know how to approach part c)

A nudge in the right direction would be greatly appreciated.

Thanks
 
Physics news on Phys.org
  • #2
Originally posted by discoverer02
A nudge in the right direction would be greatly appreciated.
Apply Gauss's Law.
 
  • #3
Again, the answer was right in front of my face.

Thanks Doc Al for pointing it out.

Up to this point I've used Gauss's Law only to find E, so since I already had E, I didn't think to use it to find Q.

I need to loosen up, open my mind and not be so intimidated when doing these problems.

Thanks again.
 

1. What is a spherical capacitor?

A spherical capacitor is a type of capacitor that consists of two concentric spherical conductors with a dielectric material between them. It is used to store electrical energy and is commonly used in electronic circuits.

2. How do you calculate the electric field of a spherical capacitor?

The electric field of a spherical capacitor can be calculated using the formula E = Q/(4πεr²), where Q is the charge on the capacitor, ε is the permittivity of the dielectric material, and r is the distance from the center of the capacitor to the point where the electric field is being calculated.

3. What is the displacement field in a spherical capacitor?

The displacement field in a spherical capacitor is a measure of the amount of electric flux that passes through a unit area of the dielectric material. It is related to the electric field by the equation D = εE, where ε is the permittivity of the dielectric material and E is the electric field.

4. How do you calculate the capacitance of a spherical capacitor?

The capacitance of a spherical capacitor can be calculated using the formula C = 4πεr, where ε is the permittivity of the dielectric material and r is the distance between the two conductors. This formula assumes that the inner conductor has a radius much smaller than the outer conductor.

5. Can a spherical capacitor have a variable capacitance?

Yes, a spherical capacitor can have a variable capacitance if the distance between the two conductors or the dielectric material is changed. This can be achieved by using a variable distance between the conductors or by using a dielectric material with a variable permittivity. This allows for the capacitance to be adjusted, making it useful in various electronic applications.

Similar threads

Replies
4
Views
276
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
14
Views
539
  • Introductory Physics Homework Help
Replies
12
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
249
  • Introductory Physics Homework Help
Replies
6
Views
2K
Back
Top