Question

An electric dipole consists of two opposite charges each of 1 MicroColumb separated by 2 cm. The dipole
is placed in an external field of 10^5 NC^-1 . Find
(1) maximum torque experienced by dipole
(2) work done in rotating the dipole through 180° starting from 0°​

Answer 1

Given ,

The two equal charges but opposite in sign 1 mc are separated by distance 2 cm

Electric field (E) = 10^5 N/C

We know that ,

The electric dipole moment is given by

$\mathtt{ \large\fbox{P = q × 2a}}$

Thus ,

P = 1 × (10)^-6 × 2 × (10)^-2

P = 2 × (10)^-8 C•m

We know that ,

The torque on a dipole in a uniform electric field is given by

$\mathtt{ \large\fbox{ Torque_{(max)} = PE \sin(90) }}$

Thus ,

Torque = 2 × (10)^-8 × (10)^5

Torque = 2 × (10)^-3 N•m

Hence , the maximum torque experienced by dipole is 2 N•m

We know that ,

The work done in rotating an electric dipole in a uniform electric field is given by

$\mathtt{ \large\fbox{ W = PE ( \cos \theta_{(1)} - \cos \theta_{(2)} )}}$

Thus ,

W = 2 × (10)^-3 × (Cos(0) - Cos(180))

W = 2 × (10)^-3 × (1 - (-1))

W = 2 × (2) × (10)^-3

W = 4 × (10)^-3 joule

Hence , the work is 4 × (10)^-3 joule

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