Question

An electric dipole is placed in a uniform electric field E with its dipole moment P parallel to the field.find
(a) the work done in turning the dipole till its dipole moment points in the direction opposite to E.
(b) the orientation of the dipole for which the torque acting on it becomes maximum.

Answer 1

Answer:

Part a)

Work done to change the orientation of dipole is given as W = 2PE

Part b)

dipole is perpendicular to the field when torque on it is maximum

Explanation:

Part a)

As we know that the dipole is placed in uniform electric field

So here potential energy of the dipole is given as

$U = - P. E$

now initial potential energy of dipole is given as

$U_i = -PE cos0$

When dipole is placed opposite to the field then we have

$U_f = - PE cos180$

now work done to change the position of dipole is given as

$W = U_f - U_i$

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

$W = 2PE$

Part b)

As we know that torque on the dipole in external field is given as

$\tau = \vec P \times \vec E$

so we have

$\tau = PE sin\theta$

so here torque is maximum when angle with the field is 90 degree

So dipole is perpendicular to the field when torque on it is maximum

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Topic : Potential energy and torque on dipole

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