Two PEC semi-infinite plates, which both are grounded (V = 0), are separated by a distance w in the x direction. A DC infinite line source of constant charge density q(x′) is positioned at x′ between the two plates and extends to infinity in the y direction. Assume the plates are infinite in the y direction and free space exists between the two plates. For this problem:
(a) Specify the appropriate boundary conditions for the potential and the associated Green’s function.
(b) Derive the Green’s function in the x-y plane in closed form.
(c) Based on this closed-form Green’s function and stated charge distribution, write an expression for the potential V(x) between the plates.
(d) Derive the Green’s function in the x-y plane in series form.
(e) Based on this series-form Green’s function and stated charge distribution, write an expression for the potential V(x) between the plates. Show all the steps.