Two small spherical balls, each of mass 10 g and carrying charges -2 μC and +2 μC, are attached to the ends of a very light rigid rod of length 20 cm. The rod is placed near an infinite non-conducting sheet having uniform surface charge density 100 μC/m², with the rod making an angle 30° with the electric field. Take ε₀ = 8.85×10⁻¹² C²/(N·m²). The magnitude of net torque on the rod is:
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Question

Two small spherical balls, each of mass 10 g and carrying charges -2 μC and +2 μC, are attached to the ends of a very light rigid rod of length 20 cm. The rod is placed near an infinite non-conducting sheet having uniform surface charge density 100 μC/m², with the rod making an angle 30° with the electric field. Take ε₀ = 8.85×10⁻¹² C²/(N·m²). The magnitude of net torque on the rod is:

Options

G1 Physics · Accepted Answer

The two opposite charges form an electric dipole of dipole moment p = qℓ. Here, q = 2×10⁻⁶ C, ℓ = 0.20 m. Thus, p = (2×10⁻⁶)(0.20) = 4×10⁻⁷ C·m. Electric field due to an infinite non-conducting sheet is E = σ/(2ε₀). With σ = 100×10⁻⁶ C/m², E = (100×10⁻⁶)/[2(8.85×10⁻¹²)] ≈ 5.65×10⁶ N/C. Dipole torque magnitude: τ = pE sin30° = (4×10⁻⁷)(5.65×10⁶)(1/2) ≈ 1.13 N·m ≈ 1.12 N·m. Therefore the physically consistent answer from the printed data is option D. The source paper prints key B (112 N·m), which…