The electric potential at any point on the central axis of a uniformly charged disk is given by Eq. 24-37,
`V= (sigma)/( 2 epsilon_(0)) ( sqrt( z^(2) + R^(2) )- z )`.
Starting with this expression, derive an expression for the electric field at any point on the axis of the disk.

Explanation

To derive the expression for the electric field \( E \) at any point on the axis of a uniformly charged disk, we start from the given electric potential \( V \):

\[ V = \frac{\sigma}{2 \epsilon_0} \left( \sqrt{z^2 + R^2} - z \right) \]

where:
- \( \sigma \) is the surface charge density,
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