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Use Gauss' Law to find the electric field

  1. Jan 28, 2009 #1
    Use Gauss' Law to find the electric field, everywhere,of charge of uniform density [itex]\rho[/itex] occupying the region [itex]a<r<b[/itex], where r is the distance from the origin. Having done this, find the potential.

    Ok, so far I said that by Gauss' Law,

    [itex]\Phi=\oint_S \vec{E} \cdot \vec{dS} = \int_V \nabla \cdot \vec{E} dV = \frac{Q}{\epsilon_0} = \frac{1}{\epsilon_0} \int_V \rho dV [/itex]

    and since V is arbitrary I obtain Poisson's Equation
    [itex]\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0} [/itex]

    I just can't see how to rearrange for E???

    Initially I was considering integrating something over a sphere of radius b and then over a sphere of radius a and subtracting them but I don't have any idea what to integrate.

    Are either of these ideas useful? If so, what do I do next? If not, can you suggest something?

  2. jcsd
  3. Jan 28, 2009 #2
    Re: Electrostatics

    What is a and b? If you are calculating the E field inside the uniformly charged sphere then the charge enclosed by the Gaussian surface is a function of the radius. Outside the sphere it can be treated as a point charge. The potential then can be found between the points a and b.
  4. Jan 28, 2009 #3


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    Homework Helper

    Re: Electrostatics

    Don't ignore the most important point of the problem. There is a symmetry that tells you the direction of E (+ or -) at every point in space, and that the magnitude of E is independent of two certain generalized coordinates.
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