Question

An electric dipole of moment p placed in

uniform electric field E has minimum potential

energy. The work done by external agent to

rotate this dipole very slowly upto which it has

maximum potential energy.

-PE

2PE

PE/2

Zero​

Answer 1

Answer:

The potential energy of the dipole is minimum, that is −pE when cosθ=1. Therefore, we can substitute 0∘ for θ. The potential energy of the dipole is zero, when the angle between dipole moment →p and electric field →E is π2.

Answer 2

Answer:

The work done by the external agent is 2PE.

Explanation:

The work done by an external agent to rotate the dipole is given as,

$W=PE(cos\theta_1-cos\theta_2)$    (1)

Where,

W=work done by an external agent

P=electric dipole moment

E=elctric field

θ₁=initial orientation

θ₂=final orientation

Initially, the dipole is in minimum potential so,

θ₁=0°

When the dipole is having maximum potential energy so,

θ₁=180°

By placing the value of θ₁ and θ₂ in equation (1) we get;

$W=PE(cos0\textdegree-cos180\textdegree)$

$W=PE(1-(-1))$

$W=2PE$

Hence, the work done by the external agent is 2PE.