Question

Consider a two-dimensional potential problem for a region bounded by four planes x=0, y=0, and y=1....

Consider a two-dimensional potential problem for a region bounded by four planes x=0, y=0, and y=1. There are no charges inside the bounded region. The boundaries at x=0, x=1, and y=0 are held at zero potential. The potential at the boundary y=1 is given by V(x,1)=V0sin(pi*x)

a.) find the electrostatic potential V(x,y) everywhere inside this region by solving the Laplace equation in two dimensions using the method of separation of variables.

b.) Calculate the surface charge density on the boundary y=0.

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