Mastering Physics Solutions: Potential of a Charged Disk

Potential of a Charged Disk

Part A = V(z) = 2kQ/a^2 * (sqrt(z^2 + a^2) – z)
Part B = E = 2kq/a^2 * (1 – (z)/sqrt(a^2 + z^2))

Solutions Below:

A disk of radius a has a total charge Q uniformly distributed over its surface. The disk has negligible thickness and lies in the xy plane. Throughout this problem, you may use the variable k in place of 1/4πε0.

Part A

What is the electric potential V(z) on the z axis as a function of z, for z > 0?
Express your answer in terms of Q, z, and a. You may use k instead of 1/4πε0.

V(z) = 2kQ/a^2 * (sqrt(z^2 + a^2) – z)

Part B

What is the magnitude of the electric field E on the z axis, as a function of z, for z > 0?
Express your answer in terms of Q, z, and a. You may use k instead of 1/4πε0.

E = 2kq/a^2 * (1 – (z)/sqrt(a^2 + z^2))

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