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NEET PHYSICSEasy

An electric dipole with dipole moment 4×1094 \times 10^{-9} C m is aligned at 3030^\circ with the direction of a uniform electric field of magnitude 5×1045 \times 10^4 NC1^{-1}. The magnitude of the torque acting on the dipole is:

A

2×1052 \times 10^{-5} N m

B

10410^{-4} N m

C

10510^{-5} N m

D

2×1042 \times 10^{-4} N m

Step-by-Step Solution

The magnitude of the torque (τ\tau) exerted on an electric dipole in a uniform electric field is given by the formula τ=pEsinθ\tau = pE \sin\theta, where pp is the dipole moment, EE is the electric field magnitude, and θ\theta is the angle between them.

Given: p=4×109p = 4 \times 10^{-9} C m E=5×104E = 5 \times 10^4 NC1^{-1} θ=30\theta = 30^\circ

Calculation: τ=(4×109)×(5×104)×sin(30)\tau = (4 \times 10^{-9}) \times (5 \times 10^4) \times \sin(30^\circ) τ=20×105×0.5\tau = 20 \times 10^{-5} \times 0.5 τ=10×105=104\tau = 10 \times 10^{-5} = 10^{-4} N m

(See NCERT Physics Class 12, Exercise 1.10).

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