Two small spherical balls of mass 10 g each with charges and , are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite non-conducting charge sheet with uniform charge density of 100 such that leng

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Solution

Q.
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 rigid rod of length 20 cm. The arrangement is now placed near an infinite non-conducting charge sheet with uniform charge density of 100 $μ C / m^{2}$ such that length of rod makes an angle of 30° with electric field generated by charge sheet. Net torque acting on the rod is: (Take $ε_{0} : 8.85 \times 10^{- 12} C^{2} / {Nm}^{2}$ ) [2025]

1 112 Nm

2 1.12 Nm

3 2.24 Nm

4 11.2 Nm

Ans.
(2)

$E = \frac{σ}{2 ε_{0}} = \frac{100 \times 10^{- 6}}{2 \times 8.85 \times 10^{- 12}} N / C$

$τ = P E \sin θ = q d E \sin θ$

$= 2 \times 10^{- 6} \times 0.2 \times \frac{100 \times 10^{- 6}}{2 \times 8.85 \times 10^{- 12}} \times \frac{1}{2}$

$\Rightarrow τ = 1.12 Nm$

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