Charged concentric metal spheres

  • #1

Homework Statement



Two concentric metal spheres have radii R1 =10cm and R2=10.5cm. The inner sphere has a charge of Q=5 nC spread uniformly over its surface, and the outer sphere has charge −Q spread uniformly over its surface.

Calculate the total energy stored in the electric field between the spheres. (Hint : the spheres can be treated as flat parallel slabs separated by 0.5cm)

Homework Equations



U = 0.5 x C x (V^2)
=(Q x V)/2

Energy Density=1/2 x epsilon_0 x E^2

The Attempt at a Solution



None, unless confused scribbles count. I know I can treat this as a parallel plate capacitor (from the hint), but that doesn't seem to help me.

I've been looking though my textbooks for hours but I can't find a clear way to work this out. I tried using (Q x d) / (A x Permittivity of air) to work out the electric field strength (E), but I didn't know which area to use for A.

If I can work out the energy density of the field, I can multiply it by the volume of the space between the spheres to find the energy stored, but again, I can't work out E.
 
Last edited:

Answers and Replies

  • #2
Andrew Mason
Science Advisor
Homework Helper
7,664
386
Use Gauss' law or Coulomb's law to calculate the field between the spheres:

[tex]\int \vec{E}\cdot dA = \frac{q_{encl}}{\epsilon_0}[/tex]

[tex]E = Q/4\pi \epsilon_0r^2[/tex]

It is not quite, but approximately equal over the .5 cm distance between spheres.

The potential difference between the spheres is V = Ed (in volts or joules/coulomb).

Since potential difference is the energy in joules per coulomb of charge: U = QV

AM
 

Related Threads on Charged concentric metal spheres

Replies
0
Views
4K
  • Last Post
Replies
12
Views
7K
Replies
3
Views
2K
  • Last Post
Replies
2
Views
1K
Replies
7
Views
21K
  • Last Post
Replies
14
Views
886
  • Last Post
Replies
8
Views
12K
  • Last Post
Replies
6
Views
6K
Replies
4
Views
3K
Top