Two small spherical balls of mass 10 g each, with charges -2 μC and 2 μC, are attached to the two ends of a very light rigid rod of length 20 cm. The arrangement is now placed near an infinite non-conducting charged sheet with uniform charge density 100 μC m⁻², such that the length of the rod makes…

Question

Two small spherical balls of mass 10 g each, with charges -2 μC and 2 μC, are attached to the two ends of a very light rigid rod of length 20 cm. The arrangement is now placed near an infinite non-conducting charged sheet with uniform charge density 100 μC m⁻², such that the length of the rod makes an angle of 30° with the electric field generated by the charge sheet. The net torque acting on the rod is (Takeε₀=8.85×10⁻¹² C² N⁻¹m⁻²)

Accepted Answer

(3) 1.12 N m. The two equal and opposite charges on a rigid rod form a dipole: p=qL=2×10⁻⁶×0.20=4×10⁻⁷ C m. An infinite non-conducting sheet gives E=σ/(2ε₀)=(100×10⁻⁶)/(2×8.85×10⁻¹²)=5.65×10⁶ N C⁻¹. Torque on a dipole: τ=pE sin θ with θ=30°. τ=4×10⁻⁷×5.65×10⁶×0.5=1.13 N m. So τ=1.13 N m; the paper prints 1.12 N m (option 3), which is 1.1299 truncated rather than rounded. (The masses play no part; they would matter only for the angular acceleration.)

Step-by-step solution

Why the other options are wrong