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    A dielectric which completely fills the volume in between two spheres is placed between two spheres. The inner sphere of radius a, carries a charge Q, the outer one is earthed. The relative permitivity of the dielectric medium varies as  1+ \frac{\alpha}{r} , where r is the distance from the centres of the spheres and alpha is a constant, show the potential is given by:


     V =\frac{Q}{4\pi\epsilon\alpha}ln(  \frac{b(r+a)}{r(b+a)})

    Can someone give me a hint as to how I should approach this?
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    You could work out the electric field via gauss' law and then find the potential from this knowing that the E field is the gradient of the potential (or even a dielectric equivalent of gauss' law which may involve the electric displacement vector D). Might go something like this:

    \displaystyle \int_S \mathbf{E}\cdot d\mathbf{S} = \int_V \frac{\rho}{\epsilon} dV \;\;;\;\; \mathbf{E} = - \nabla V
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    Find the D field, and thus the E field, and thus the potential.
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    Have you got it?
 
 
 
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