# Semi-Infinite planes at an angle

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1. Jun 28, 2015

This problem was on my exam last week, and i've been having some troubles coming up with a solution.

1. The problem statement, all variables and given/known data

Two semi-infinite conducting planes are connected by insulating glue, they make a 30º angle with each other. One of them is at ground potential, and the other one at V0. Find the potential between the conductors.
Note: There might be solutions, in which the potential has logarithmic dependence on the distance to the axis, or even independent of this distance.
2. Relevant equations
Laplace's equation in cylindrical coordinates.
3. The attempt at a solution

The boundary conditions i came up with are:
1- V=0 at phi=0
2- V=V0 at phi=alpha

But i'm note sure if this is right.

2. Jun 28, 2015

### TSny

Your work looks correct to me. But you might be required to justify ignoring the parts of the Laplacian that involve derivatives of the radial variable $s$ and derivatives of the variable $z$.

Of course, you can make your answer more specific by substituting the given value for $\alpha$.

Last edited: Jun 28, 2015
3. Jul 2, 2015

Use the fact that the potential for $\alpha = 0$ or $\alpha = 30^0$ is independent of $s$ along with the general form of the solution for $V$ using separation of variables: $V(s, \alpha, z) = f(s)g(\alpha)h(z)$.