An electric dipole of moment p is Iying along a uniform electric field E. The work done in rotating the dipole by 90° is

Question

An electric dipole of moment p is Iying along a uniform electric field E. The work done in rotating the dipole by 90° is (A)  √ 2 p E (B)  ( p E/ 2) (C) 2 pE (D) pE

Tardigrade Admin · Accepted Answer

When an electric dipole is placed in an electric field

E

,
a torque

τ = p \times E

acts on it.
This torque tries to rotated the dipole through an angle

θ

.
If the dipole is rotated from an angle

θ_{1}

to

θ_{2}

,
then work done by external force is given by

W = pE (cos θ_{1} - cos θ_{2})

Putting

θ_{1} = 0^{\circ}, θ_{2} = 9 0^{\circ}

in the Eq. (i), we get

W = pE (cos 9 0^{\circ} - cos 9 0^{\circ})

= pE (1 - 0)

= pE

Q. An electric dipole of moment $p$ is Iying along a uniform electric field $E$ . The work done in rotating the dipole by $9 0^{\circ}$ is

$2 pE$

$\frac{pE}{2}$

$2 pE$

$pE$

Q. An electric dipole of moment p is Iying along a uniform electric field E. The work done in rotating the dipole by 90∘ is

2​pE

2pE​

2pE

pE

Q. An electric dipole of moment $p$ is Iying along a uniform electric field $E$ . The work done in rotating the dipole by $9 0^{\circ}$ is

$2 pE$

$\frac{pE}{2}$

$2 pE$

$pE$