- #1

zengodspeed1

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## Homework Statement

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There is a conducting cone with angle α placed so that its vertex is normal to an electrically grounded plate, but electrically insulated from the plate and kept at a constant potential V. Find the potential V and the electric field in the region between the cone and the plate. End effects of the cone are neglected. V is independent of r and φ.

## Homework Equations

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If V is independent of r and Φ we know that the Laplacian reduces to:

we have the boundary condition:

## The Attempt at a Solution

Firstly, rearranging the Laplacian to solve for dV:

and integrating with respect to theta gives:

Using the boundary condition for the cone:

I don't really know how I can include the plane into my calculations. Any help would be very much appreciated.