Two small spherical balls of mass 10 g each with charges -2 μ C and...

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_0: 8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2

)

Two small spherical balls of mass 10 g each with charges -2 μ C and 2 μ C , are attached to two ends of very light

Options

A112 Nm
B1.12 Nm
C2.24 Nm
D11.2 Nm

Correct answer

B. 1.12 Nm

Step-by-step solution

\begin{aligned} \mathrm{E} & =\frac{\sigma}{2 \varepsilon_0} \\ \tau & =\mathrm{PE} \sin \theta\end{aligned}

\begin{aligned} & =\left[\left(2 \times 10^{-6}\right)\left(\frac{2}{10}\right)\right]\left[\frac{100 \times 10^{-6}}{2 \times 8.85 \times 10^{-12}}\right]\left(\frac{1}{2}\right) \\ & =\frac{10}{8.85}=1.12 \mathrm{Nm}\end{aligned}

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