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 ea23bc0d 0e6b 4507 b5fb 1f5d9f0cb05f 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 c7867e5b 1603 481e 9e51 89896d3a93e9 0 and φ c7867e5b 1603 481e 9e51 89896d3a93e9 2π. Note that you cannot accept solutions for 986ceefd f57d 446d a698 a7363f0a15b5 of negative powers in r.

(b) Match the boundary condition at 4c429672 6952 4eb6 a8a0 69a01f4618f6

(c) One of the terms in this solution has an electric field intensity that is infinite at the tip of the fin, where1f6f8c29 98fe 4b41 9ccb fe9c2a7d7201 Sketch 986ceefd f57d 446d a698 a7363f0a15b5 and e103a37b d0ac 4586 94a1 ee88333755b3 in the neighborhood of the tip. What is the a42a4ae5 cf55 4d36 9132 c257842264b3 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

b5572d0c fca8 45fc ae76 e0f5b1b4d754

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