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Physics Question on Electric charges and fields

An electric dipole consists of two opposite charges each 0.05 μ\muC separated by 30 mm. The dipole is placed in an uniform external electric field of 106 NC−1 10^6 \, NC^{ - 1}. The maximum torque exerted by the field on the dipole is

A

6×10−3 N−m−1 6 \times 10^{ - 3} \, N -m^{ - 1}

B

3×10−3 N−m−1 3 \times 10^{ - 3} \, N -m^{ - 1}

C

15×10−3 N−m−1 15 \times 10^{ - 3} \, N -m^{ - 1}

D

1.5×10−3 N−m−1 1.5 \times 10^{ - 3} \, N -m^{ - 1}

Answer

1.5×10−3 N−m−1 1.5 \times 10^{ - 3} \, N -m^{ - 1}

Explanation

Solution

Given q=0.05μC=5×10−8Cq = 0.05 \mu C = 5 \times 10^{ - 8 } C
2a = 30 nm = 0.03 m
E = 106 NC−1 10^6 \, NC^{ - 1}
Torque acting on an electric dipole placed in an uniform electric field
τ=pE sin θ\tau = pE \, sin \, \theta
For maximum torque θ=90∘ \theta = 90^\circ
∴τmax=pE\therefore \tau_{ max} = pE
= E (q×2a) ( q \times 2a)
= 106×5×10−8 ×0.03 10^6 \times 5 \times 10^{ - 8 } \, \times 0.03
= 1.5×10−3 N−m−1 1.5 \times 10^{ - 3} \, N -m^{ - 1}