An electric dipole of moment p is placed at an angle of π/3 with a uniform electrical field E. If after sometime the dipole is tilted further by π/6, the total work done in changing the position of dipole is:

The correct answer is option 3) i.e. 0.5pE

CONCEPT:

• Work done in rotating a dipole in an electric field:
  • ​Consider an electric dipole placed in a uniform electric field E as shown.

• The force due to each of the charges is qE and -qE creating a zero net force. Since they are separated by a distance, a torque is produced. 

Torque, τ = Force × perpendicular distance between charges = qE × 2l sinθ 

Electric dipole moment is given by: p = q × 2l

⇒ τ = pEsinθ = p × E

• Work Done to turn an electric dipole from θ1 to θ2 is given by:

WD = \(\int^{θ_2}_{θ_1} \tau.dθ= \int^{θ_2}_{θ_1}pEsinθ dθ =[pEcosθ]_{θ_1}^{θ_2}\)

⇒ Work Done = pE [cosθ1 - cosθ2]

CALCULATION:

Given that:

Initially, the dipole is at an angle θ₁ = π/3

When the dipole is further tilted by π/6, at the final position θ₂ = π/3 + π/6 = π/2

Work Done to turn an electric dipole from θ1 to θ2 = pE [cosθ1 - cosθ2] = pE [cos(π/3) - cos(π/2)] = pE[0.5 - 0] = 0.5pE