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Two point charges – q and + q are located atpoints (0,0, $- α$ ) and (0,0, $α$ ) respectively. The electric potential at a point (0,0,z), where z> $α$ is

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$\frac{qα}{4 {πϵ}_{0} z^{2}}$

$\frac{q}{4 {πϵ}_{0} α}$

$\frac{2 qα}{4 {πϵ}_{0} (z^{2} - α^{2})}$

$\frac{2 qα}{4 {πϵ}_{0} (z^{2} + α^{2})}$

answer is C.

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Detailed Solution

$\begin{array}{l} V_{Z} = \frac{1}{4 {πε}_{0}} \frac{q}{(z - α)} + \frac{1}{4 {πε}_{0}} {(\frac{- q}{Z + α})}^{Z} \\ = \frac{2}{4 {πε}_{0}} (\frac{1}{z - α} - \frac{1}{z + α}) = \frac{2 αq}{4 {πε}_{0} (z^{2} - α^{2})} \end{array}$

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