An electric dipole of dipole moment p is lying along uniform electric field E. Calculate the work done in rotating the dipole by 90 degrees.

Ques: An electric dipole of dipole moment p is lying along uniform electric field E. Calculate the work done in rotating the dipole by 90 degrees.

Ans: The work done in rotating the dipole by 90 degrees when dipole moment is lying along uniform electric field is “pE”. 

Explanation: The potential energy of an electric dipole in a uniform electric field is given by an expression: U = -pEcosθ.

• where p is the dipole moment,
• E is the electric field strength,
• θ is the angle between the dipole moment and the electric field.

Initially, the dipole moment is aligned with the electric field, so θ = 0, and the potential energy is:

U1 = -pEcos0 = -pE

When the dipole is rotated by 90 degrees, the angle between the dipole moment and the electric field becomes θ = 90 degrees, and the potential energy becomes:

U2 = -pEcos90 = 0

The change in potential energy is then equal to the work done

Work Done = ΔU = U2 - U1 = 0 - (-pE) = pE

Therefore, the potential energy of the dipole in rotating it by 90 degrees is pE.