Question

An electric dipole of moment \(\mu = 400\,\mu C\,m\) is placed in a transverse electric field \(E = 50\,V/m\) at an angle of \(30^\circ\). Then a torque of

• A. \(10^{-2}\) Nm acts along the direction of \(\vec{E}\)
• B. \(10^{-3}\) Nm acts along the direction of \(\vec{\mu}\)
• C. \(10^{-5}\) Nm acts normal to both \(\vec{E}\) and \(\vec{\mu}\)
• D. \(10^{-3}\) Nm acts along the direction of \(\vec{E}\)
• E. \(10^{-2}\) Nm acts normal to both \(\vec{E}\) and \(\vec{\mu}\)

Hint:

Torque on dipole is maximum when perpendicular to field.

Answer 1

Answer: (E)

Concept: Torque on dipole: \[ \tau = pE \sin \theta \] Direction is perpendicular to both \(\vec{p}\) and \(\vec{E}\).

Step 1: Convert dipole moment. \[ p = 400 \,\mu C m = 400 \times 10^{-6} = 4 \times 10^{-4} \]

Step 2: Substitute values. \[ \tau = (4 \times 10^{-4})(50)\sin 30^\circ \]

Step 3: Simplify. \[ \tau = 4 \times 10^{-4} \times 50 \times \frac{1}{2} = 4 \times 10^{-4} \times 25 = 10^{-2} \]

Step 4: Direction. Torque direction is perpendicular to both \(\vec{E}\) and \(\vec{\mu}\).

Step 5: Conclusion. \[ \boxed{10^{-2}\,\text{Nm, perpendicular to both}} \]