Question

The magnitude of the torque experienced by an electric dipole of dipole moment \(P\) placed at an angle of \(30^\circ\) in a uniform electric field \(E\) is

• A. \(PE\)
• B. \(\frac{\sqrt{3}}{2}PE\)
• C. \(\frac{PE}{2}\)
• D. \(\frac{PE}{\sqrt{2}}\)
• E. \(\frac{PE}{\sqrt{3}}\)

Hint:

Torque on a dipole is maximum at \(90^\circ\) and zero at \(0^\circ\). Always use \(\tau = PE\sin\theta\).

Answer 1

The Correct Option is C

Step 1: Recall the formula for torque on an electric dipole.
The torque \(\tau\) experienced by an electric dipole in a uniform electric field is given by:
\[ \tau = PE \sin\theta \] where \(P\) is dipole moment, \(E\) is electric field, and \(\theta\) is the angle between them.

Step 2: Identify the given angle.
Here, \[ \theta = 30^\circ \]

Step 3: Substitute into the formula.
\[ \tau = PE \sin 30^\circ \]

Step 4: Recall the value of \(\sin 30^\circ\).
\[ \sin 30^\circ = \frac{1}{2} \]

Step 5: Calculate the torque.
\[ \tau = PE \times \frac{1}{2} \] \[ \tau = \frac{PE}{2} \]

Step 6: Interpret the result.
The torque depends on the sine of the angle, so it reduces when the dipole is not perpendicular to the field.

Step 7: Final answer.
\[ \boxed{\frac{PE}{2}} \] which matches option \((3)\).