# Potential Equation on a Disc : Dirichlet

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Solve the potential equation on a disc...

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Solution:

We have to solve a Dirichlet problem inside a circle of radius (c).

The most usual method to do that is the Fourier method, that means using separation of variables.

Let's process our equation and let's separate the variables:

( 1)

Let

( 2)

Introducing in (1), we will have

( 3)

Why should we use a positive constant and not a negative one?

Because using a negative constant, the ODE in (T) doesn't have periodic solutions, while our problem must have periodic solutions with ...

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