This question refers to problem Ch4-7P from Field and Wave Electromagnetics by D

Question

This question refers to problem Ch4-7P from Field and Wave Electromagnetics by David K Cheng. This question refers to part b of the problem. In part A I am asked to find the surface charge density on a conducting plate. In part b I am asked to use that surface charge density to find the total charge on the plate. THe solution manual gives the following integral as the proper equation relating surface charge to total charge Q.

The surface charge rho(sub_s) is:

My question is why there is a 2(pi)r dr term in the above integral. To relate charge to surface charge, I should just have to multiply the surface charge density by the surface area of the conducting plate, however 2(pi)r is the surface area of a cylinder not the surface area of a flat conducting plate. Could you please explain why the integral was set up the way it is. Specifically where the 2(pi)r term comes from.

Thank You

Explanation / Answer

for cylindrical cordinate ds = 2*pi*rdr

q = surface integral of charge density and surface area

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