Question

Find the electrostatic potential in the disk r <1 corresponding to the boundary value
u(O) = sine^3 0

Answer 1

Step-by-step explanation:

If the potential is speciÖed on a closed surface, the potential o§ the surface is uniquely deter-

mined in terms of the surface potential. This is known as Dirichletís boundary value problem and

most problems we will consider belong to this category. Solving Dirichletís problems is greatly

facilitated by Önding a suitable Greenís function for a given boundary shape. However, except

for simple geometries (e.g., plane, sphere, cylinder, etc.), Önding Greenís functions analytically is

not an easy task. For complicated electrode shapes, potential problems often have to be solved

numerically.

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