Figure P5.8.7 shows a circular cylindrical wall having potential relative to a grounded fin in…
Figure P5.8.7 shows a circular cylindrical wall having potential 
relative to a grounded fin in the plane φ = 0 that reaches from the wall to the center. The gaps between the cylinder and the fin are very small.
(a) Find all solutions in polar coordinates that satisfy the boundary conditions at φ 
0 and φ 2π. Note that you cannot accept solutions for 
of negative powers in r.
(b) Match the boundary condition at 
(c) One of the terms in this solution has an electric field intensity that is infinite at the tip of the fin, where
Sketch and 
in the neighborhood of the tip. What is the 
on the fin associated with this term as a function of r? What is the net charge associated with this term?
(d) Sketch the potential and field intensity throughout the region.
Figure P5.8.7
