KCET · Physics · Electrostatics

An electric dipole with dipole moment \(4 \times 10^{-19} \mathrm{C}-\mathrm{m}\) is aligned at \(30^{\circ}\) with the direction of a uniform electric field of magnitude \(5 \times 10^4 \mathrm{NC}^{-1}\), the magnitude of the torque acting on the dipole is

A \(\sqrt{3} \times 10^{-4} \mathrm{~N}-\mathrm{m}\)
B \(10^{-5} \mathrm{~N}-\mathrm{m}\)
C \(10 \times 10^{-3} \mathrm{~N}-\mathrm{m}\)
D \(10^{-4} \mathrm{~N}-\mathrm{m}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(10^{-4} \mathrm{~N}-\mathrm{m}\)

Step-by-step Solution

Detailed explanation

Given, for an electric dipole, dipole moment, \(p=4 \times 10^{-9} \mathrm{C}\) \(\theta=30^{\circ}\)
Magnitude of electric field, \(E=5 \times 10^4 \mathrm{~N} / \mathrm{C}\)
\(\therefore\) Torque, \(\tau=p E \sin \theta\)
\(=4 \times 10^{-9} \times 5 \times 10^4 \sin 30^{\circ}=10^{-4} \mathrm{~N}-\mathrm{m}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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