If the net electric field at point P along Y axis is zero, then the ratio of is , where

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Solution

Q.
If the net electric field at point P along Y axis is zero, then the ratio of $| \frac{q_{2}}{q_{3}} |$ is $\frac{8}{5 \sqrt{x}}$ , where $x$ = ______ . [2024]

Ans.
(5)

$\frac{K q_{2}}{{(\sqrt{20})}^{2}} \cos β = \frac{K q_{3}}{{(5)}^{2}} \cos θ$

$\frac{K q_{2}}{20} \frac{4}{\sqrt{20}} = \frac{K q_{3}}{25} \frac{4}{\sqrt{25}}$

$\frac{q_{2}}{q_{3}} = \frac{20}{25} \frac{\sqrt{20}}{\sqrt{25}} = \frac{8}{5 \sqrt{x}}$

$\Rightarrow \sqrt{x} = \frac{8 \times 25 \sqrt{25}}{5 \times 20 \sqrt{20}} \Rightarrow x = 5$

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