# Solved Problem-3

Problem-3
Region between the two coaxial cones is shown in Fig. A potential V1 exists at Î¸1 and V = 0 at Î¸2. The cone vertices are insulated at r = 0. Solve Laplaceâ€™s equation to get potential at a cone at any angle Î¸.
Arrangement for problem

Solution
Since V varies with Î¸ only, Laplaceâ€™s equation can be written as,

Integrating,

Integrating once again,

where, A and B are constants.

Applying boundary conditions, we get,
At
At

Solving for A and B,

Substituting the values of A and B and rearranging, we get,