JEE Main · 2025 · 04 Apr 2025 · Shift 1 · Electrostatics

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 nonconducting charge sheet with uniform charge density of

100 μ C / m^{2}

such that length of rod makes an angle of

3 0^{\circ}

with electric field generated by charge sheet. Net torque acting on the rod is:
(Take

ε_{o} : 8.85 \times 1 0^{- 12} C^{2} / Nm^{2}

)

(A)112 Nm
(B)1.12 Nm✓ Correct
(C)2.24 Nm
(D)11.2 Nm

Answer: (B)

Solution

The infinite sheet produces a uniform field

E = σ /2 ε_{0}

, so the two equal and opposite charges on the rigid rod form an electric dipole in a uniform field and experience only a torque. The dipole moment is

p = q d = (2 \times 1 0^{- 6}) (0.2) = 4 \times 1 0^{- 7} C\cdotm

, and the field is

E = \frac{100 \times 1 0 ^{- 6}}{2 ( 8.85 \times 1 0 ^{- 12} )} = 5.65 \times 1 0^{6} N/C .

The torque is

τ = pE sin θ = (4 \times 1 0^{- 7}) (5.65 \times 1 0^{6}) sin 3 0^{\circ} \approx 1.12 N\cdotm .

The net torque on the rod is about

1.12

N·m.

JEE Main · 2025 · 04 Apr 2025 · Shift 1 · Single correct option

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JEE Main · 2025 · 04 Apr 2025 · Shift 1 · Electrostatics

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