An electric dipole placed in an electric field of intensity 2 × 10⁵...

Question

An electric dipole placed in an electric field of intensity 2 × 10⁵ N/C at an angle of 30° experiences a torque equal to 4 N·m. The charge on the dipole of dipole length 2 cm is:

Accepted Answer

Given:
E = 2 × 10⁵ N/C
θ = 30°
τ = 4 N·m
2l = 2 cm = 0.02 m

Formulas:
Torque: τ = pE sinθ
Dipole moment: p = q × (2l)

Combined formula:
τ = q × (2l) × E × sinθ

Rearrange for q:
q = τ / [(2l) × E × sinθ]

Substitute values:
q = 4 / [0.02 × 2 × 10⁵ × sin30°]
q = 4 / [0.02 × 2 × 10⁵ × 0.5]
q = 4 / 2000
q = 2 × 10⁻³ C = 2 mC

Answer: Option (C) 2 mC

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