An electric dipole of dipole moment $6 \times 10^{-6} \mathrm{Cm}$ is placed in uniform electric field of magnitude $10^{6} \mathrm{~V} / \mathrm{m}$. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ______ J.

JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Electrostatics

An electric dipole of dipole moment

6 \times 1 0^{- 6} Cm

is placed in uniform electric field of magnitude

1 0^{6} V / m

. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ______ J.

Answer: 12

Solution

The potential energy of a dipole of moment

p

in a uniform field

E

U = - pE cos θ

The work done to rotate the dipole from an initial orientation to a final orientation equals the change in this potential energy:

W = U_{f} - U_{i} = - pE cos θ_{f} - (- pE cos θ_{i})

Here

θ_{i} = 0^{\circ}

(moment parallel to field) and

θ_{f} = 18 0^{\circ}

(moment antiparallel):

W = - pE (- 1) - (- pE (1)) = pE + pE = 2 pE

Substituting

p = 6 \times 1 0^{- 6} C\cdotm

and

E = 1 0^{6} V/m

W = 2 \times 6 \times 1 0^{- 6} \times 1 0^{6} = 12 J

JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Integer answer

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JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Electrostatics

Solution

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