Two equal positive point charges are separated by a distance 2a. The distance of a point from the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge q₀ becomes maximum is $\frac{a}{\sqrt{x}}$ . The value of $x$ is _______.

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answer is 2.

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Detailed Solution

$\begin{array}{l} F_{net} = 2 Fcos θ \\ = \frac{2 {Kq}_{0} Qx}{{(a^{2} + x^{2})}^{3 / 2}} \end{array}$
For maxima, $\frac{d}{dx} (\frac{2 {Kq}_{0} Qx}{{(a^{2} + x^{2})}^{3 / 2}}) = 0$
we get, $x = \frac{a}{\sqrt{2}}$

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