# Solved Problem-3

Problem-3

Region between the two coaxial cones is shown in Fig. A potential

*V*_{1}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
Integrating,
Integrating once again,
where,
Applying boundary conditions, we get,

At

At
Solving for
Substituting the values of

*V*varies with*Î¸*only, Laplaceâ€™s equation can be written as,*A*and*B*are constants.At

At

*A*and*B*,*A*and*B*and rearranging, we get,