# The Potential of a Disk With a Certain Charge Distribution

Please see the attach file for the question taken from "Classical Electrodynamics 3rd by Jackson".

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#### Solution Preview

First, let's calculate the potential along the z-axis.

The charge surface density is given by:

(1.1)

Where K is some constant to be determined later.

The potential along the z axis is given by (in polar coordinates):

(1.2)

The angular integration just gives a factor of , so:

(1.3)

Setting

(1.4)

Therefore:

(1.5)

This is a conducting disk, hence the potential over the disk is constant V, specificaly ...

#### Solution Summary

The solution shows in detail how to find the potential everywhere using Legendre expansion once we know the potential on the z axis.

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