$\begin{array}{rcl}\mathbf{-}\frac{\mathbf{dV}}{\mathbf{dx}}& \mathbf{=}& \mathbf{-}\frac{\mathbf{d}}{\mathbf{d}\mathbf{x}}\mathbf{\left(}\frac{\mathbf{\sigma}}{\mathbf{2}{\mathbf{\epsilon}}_{\mathbf{0}}}\mathbf{\right(}\sqrt{{\mathbf{R}}^{\mathbf{2}}\mathbf{+}{\mathbf{x}}^{\mathbf{2}}}\mathbf{-}\mathbf{x}\mathbf{\left)}\mathbf{\right)}\\ & \mathbf{=}& \mathbf{-}\frac{\mathbf{\sigma}}{\mathbf{2}{\mathbf{\epsilon}}_{\mathbf{0}}}\frac{\mathbf{d}\mathbf{(}\sqrt{{\mathbf{R}}^{\mathbf{2}}\mathbf{+}{\mathbf{x}}^{\mathbf{2}}}\mathbf{-}\mathbf{x}\mathbf{)}}{\mathbf{d}\mathbf{x}}\end{array}$

A disk with radius *R* has uniform surface charge density *σ*.

By regarding the disk as a series of thin concentric rings, the electric potential *V* at a point on the disk's axis a distance *x* from the center of the disk is

Derive an expression for −∂*V*/∂*x*.

Express your answer in terms of the given quantities and appropriate constants.

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