Calculation of electric field from a set of equipotential surfaces

[kihr]

Homework Statement

A set of concentric hemispherical surfaces is given, each of which is an equipotential surface. These concentric surfaces do not, however, have the same value of potential, and the potential difference between any two surfaces is also not constant. The surfaces are spaced apart at the same radial distance between each other. I need to find the direction and value of the electric field in this region.

Homework Equations

The electric field will be in the radial direction as the field has to be normal to the equipotential surface at each point. Its direction will be along the negative gradient of the potential (E = - dV/dr).

The Attempt at a Solution

I need some clues as to how to calculate the value of the electric field. This would have been easy if the relation between V and r were known. I guess this needs to be derived. Please give me some hints as to how to tackle this. Thanks.

 

[lanedance]

take a guassian surface with no charge inside to convince yourself the field decreases with 1/r^2, between any 2 plates

then take a radial line integral of the field, which must be equal to the potential difference to solve for E

 

[kihr]

With your tips I was able to solve the problem. Many thanks.