Question 727: Electrostats & Capacitance

Question

As shown in the figure, a configuration of two equal point charges $$\left(q_{0}=+2 \mu \mathrm{C}ight)$$ is placed on an inclined plane. Mass of each point charge is $$20 \mathrm{~g}$$. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height $$\mathrm{h}=x 	imes 10^{-3} \mathrm{~m}$$.
The value of $$x$$ is ____________.
(Take $$\frac{1}{4 \pi \varepsilon_{0}}=9 	imes 10^{9} \mathrm{~N} \mathrm{~m}^{2} \mathrm{C}^{-2}, g=10 \mathrm{~m} \mathrm{~s}^{-2}$$ )

Accepted Answer

For equilibrium along the plane
$$
\begin{aligned}
& \mathrm{mg} \sin 	heta=\frac{1}{4 \pi \epsilon_0} 	imes \frac{\mathrm{q}_0^2}{\left(\mathrm{~h} \operatorname{cosec} 30^{\circ}ight)^2} \\
& 	herefore \mathrm{h}^2=\frac{1}{4 \pi \epsilon_{\mathrm{o}}} 	imes \frac{\mathrm{q}_0^2}{\mathrm{mg} \operatorname{cosec} 30^{\circ}} \\
& =9 	imes 10^9 	imes \frac{\left(2 	imes 10^{-6}ight)^2}{0.02 	imes 10 	imes 2} \\
& 	herefore \mathrm{h}=3 	imes 10^4 	imes \frac{2 	imes 10^{-6}}{0.2} \\
& =0.3 \mathrm{~m} \\
& =300 \mathrm{~mm}
\end{aligned}
$$

Electrostats & Capacitance

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