Question

An electric dipole consists of two opposite charges each 0.05 $\mu$C separated by 30 mm. The dipole is placed in an uniform external electric field of $ 10^6 \, NC^{ - 1}$. The maximum torque exerted by the field on the dipole is

• A. $ 6 \times 10^{ - 3} \, N -m^{ - 1}$
• B. $ 3 \times 10^{ - 3} \, N -m^{ - 1}$
• C. $ 15 \times 10^{ - 3} \, N -m^{ - 1}$
• D. $ 1.5 \times 10^{ - 3} \, N -m^{ - 1}$

Answer 1

The Correct Option is D

Given $ q = 0.05 \mu C = 5 \times 10^{ - 8 } C $
2a = 30 nm = 0.03 m
E = $ 10^6 \, NC^{ - 1}$
Torque acting on an electric dipole placed in an uniform electric field
$ \tau = pE \, sin \, \theta $
For maximum torque $ \theta = 90^\circ$
$\therefore \tau_{ max} = pE$
= E $ ( q \times 2a)$
= $ 10^6 \times 5 \times 10^{ - 8 } \, \times 0.03$
= $ 1.5 \times 10^{ - 3} \, N -m^{ - 1}$