1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Charged concentric metal spheres

  1. Oct 26, 2009 #1
    1. The problem statement, all variables and given/known data

    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)

    2. Relevant equations

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

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

    3. 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: Oct 26, 2009
  2. jcsd
  3. Oct 26, 2009 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    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

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook