Question

An electric dipole with dipole moment 4 x 10^-9 Cm is aligned at 30 degree with the direction of the uniform electric field of magnitude 5 x 10⁴ NC^-1. The magnitude of the torque acting on the diapole is 

• A. 10^-5 Nm
• B. 10^-4 Nm
• C. 10 x 10^-3 Nm
• D. √ 3 x 10^-4 Nm

Answer 1

The Correct Option is B

 The torque acting on an electric dipole in a uniform electric field is given by the formula:

\( \tau = pE \sin \theta \)

Given:

• Dipole moment (p): \( 4 \times 10^{-9} \, \text{Cm} \)
• Electric field (E): \( 5 \times 10^4 \, \text{N/C} \)
• Angle (θ): \( 30^\circ \)

Step 1: Substitute the given values into the formula:

\( \tau = (4 \times 10^{-9} \, \text{Cm})(5 \times 10^4 \, \text{N/C}) \sin(30^\circ) \)

Step 2: Use the value of \( \sin(30^\circ) = \frac{1}{2} \):

\( \tau = (4 \times 10^{-9} \, \text{Cm})(5 \times 10^4 \, \text{N/C}) \times \frac{1}{2} \)

Step 3: Simplify the expression:

\( \tau = (20 \times 10^{-5} \, \text{Cm}) \times \frac{1}{2} = 10 \times 10^{-5} \, \text{Nm} \)

Therefore, the magnitude of the torque acting on the dipole is: \( 10^{-4} \, \text{Nm} \). The correct answer is (B) \( 10^{-4} \, \text{Nm} \).