Question 319: Electrostats & Capacitance

Question

Two small spherical balls of mass 10 g each with charges $-2 \mu \mathrm{C}$ and $2 \mu \mathrm{C}$, are attached to two ends of very light rigid rod of length 20 cm . The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of $100 \mu \mathrm{C} / \mathrm{m}^2$ such that length of rod makes an angle of $30^{\circ}$ with electric field generated by charge sheet. Net torque acting on the rod is:
(Take $\varepsilon_{\mathrm{o}}: 8.85 	imes 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$ )

Accepted Answer

$$\begin{aligned}
& \mathrm{E}=\frac{\sigma}{2 \varepsilon_0} \
& 	au=\mathrm{PE} \sin 	heta \
& =\left[\left(2 	imes 10^{-6}ight)\left(\frac{2}{10}ight)ight]\left[\frac{100 	imes 10^{-6}}{2 	imes 8.85 	imes 10^{-12}}ight]\left(\frac{1}{2}ight) \
& =\frac{10}{8.85}=1.12 \mathrm{Nm}
\end{aligned}$$

Answer

1.12 Nm

Answer

2.24 Nm

Answer

11.2 Nm

Answer

112 Nm

Electrostats & Capacitance

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