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If the net electric field at point $\mathrm{P}$ along $\mathrm{Y}$ axis is zero, then the ratio of $\left|\frac{q_2}{q_3}\right|$ is $\frac{8}{5 \sqrt{x}}$, where $x=$ _____.
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The correct answer is:
5
$\begin{aligned} & \frac{\mathrm{Kq}_2}{20} \cos \beta=\frac{\mathrm{Kq}_3}{25} \cos \theta \\ & \frac{\mathrm{Kq}_2}{20} \frac{4}{\sqrt{20}}=\frac{\mathrm{Kq}_3}{25} \frac{4}{\sqrt{25}} \\ & \frac{\mathrm{q}_2}{\mathrm{q}_3}=\frac{20}{25} \sqrt{\frac{20}{25}}=\frac{8}{5 \sqrt{\mathrm{x}}} \\ & \Rightarrow \sqrt{\mathrm{x}}=\frac{8 \times 25 \sqrt{25}}{5 \times 20 \sqrt{20}} \\ & \mathrm{x}=5\end{aligned}$
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