An electric dipole of dipole moment p is placed parallel to a uniform electric field E. The work done required to rotate the dipole by an angle 180° will be:

CONCEPT:

Electric dipole

• When two equal and opposite charges are placed at a very small distance to each other then this arrangement is called an electric dipole. 
• The electric dipole moment is defined as the product of the magnitude of one charge and the distance between the charges in an electric dipole.

⇒ P = q × 2r    

Where 2r = distance between the two charges

• Work done required to rotate an electric dipole in an external uniform electric field from the angle θ₁ to θ₂ is given as,

⇒ W = pE(cosθ₁ - cosθ₂)

Where θ₁ and θ₂ = initial and the final angle between the dipole and the electric field

CALCULATION:

Given p = dipole moment, E = electric field

• When the electric dipole is placed parallel to the electric field the angle between the dipole and the electric field is given as,

⇒ θ1 = 0°

When the dipole is rotated by an angle of 180°,

⇒ θ2 = 180°

So the work done is given as,

⇒ W = pE(cosθ1 - cosθ2)

⇒ W = pE(cos 0° - cos180°)

⇒ W = pE(1 - (-1))

⇒ W = pE(1 +1)

⇒ W = 2pE

• Hence, option 1 is correct.