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What will be the magnitude of the torque on an electric dipole of dipole moment 4×10⁻⁹ C m placed in a uniform electric field of intensity 5×10⁴ N C⁻¹, making an angle of 180° with the field?

Asked in GSEB Board March 2018 · Torque, energy and work done

• (1) 10⁻⁴ N m
• (2) 0 (zero)
• (3) 2×10⁻⁴ N m
• (4) 10⁻⁶ N m

Step-by-step solution

Why the other options are wrong

• (1) No slip at 180° gives 10⁻⁴ N m: it is pE sin 30°, the torque this dipole would feel at 30° (the textbook version of this problem). At 180°, sin 180° = 0.
• (3) This is pE = (4×10⁻⁹)(5×10⁴) = 2×10⁻⁴ N m, which leaves out sin θ (or uses |cos 180°| = 1 in its place). That is the torque at 90°, not at 180°.
• (4) No single slip gives 10⁻⁶ N m. Sanity check: the largest torque this dipole can feel is pE = 2×10⁻⁴ N m, and at 180° the torque is exactly zero.

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