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Potential on the axis of a hollow cylinder

Potential on the axis of a hollow cylinder

Grade:12

1 Answers

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

Dear student,

dV = K dQ / r, let dQ = sigma dA, use a geometric argument to get r. Your dA here is going to have fixed radius (call it R ), so dA = R dz dphi. You have angular symmetry, so the integration of d phi is 2 pi. This combines with K = 1 / (4 pi epsilon). Your integration of dz will run from -L/2 to L/2.

As a check, when z goes to infinity, you should get it to look like a point charge. Probably by binomial expansion.

 

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Sagar Singh

B.Tech, IIT Delhi



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