Discussion
If the torque acting on an electric dipole when placed at an angle 30° with the direction of an uniform electric field is τ, then the torque acting on the same dipole when placed in the same field at an angle 45° is
Answer: D
The new torque is \(\sqrt{2}\tau\).
The torque on a dipole is \(pE\sin\theta\), so
\[ \begin{aligned} \frac{\tau'}{\tau} \\ &= \frac{\sin 45^{\circ}}{\sin 30^{\circ}} \\ &= \frac{1/\sqrt{2}}{1/2} \\ &= \sqrt{2} \end{aligned} \]
\(\frac{1}{\sqrt{2}}\tau\) inverts the ratio, and \(2\tau\) or \(\frac{1}{2}\tau\) use the angles in proportion instead of their sines.
The torque is greatest at \(90^{\circ}\), where it equals \(pE = 2\tau\).
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