Question

An electric dipole of dipole moment is 6.0 x 10^-6 Cm placed in a uniform electric field of 1.5 x 10³ NC^-1 in such a way that dipole moment is along electric field. The work done in rotating dipole by 180º in this field will be _____mJ.

Hint:

Work done depends on the angle of rotation and the strength of the electric field.

Answer 1

Correct Answer: 18

Step 1: Formula for work done - Work done is given by: \[ W_{\text{ext}} = U_f - U_i, \] where \(U = -\vec{P} \cdot \vec{E}\). - Initial potential energy: \[ U_i = -PE \cos 0 = -PE. \] - Final potential energy: \[ U_f = -PE \cos 180 = +PE. \]

Step 2: Substitute the values - \[ W_{\text{ext}} = U_f - U_i = PE - (-PE) = 2PE. \] Substituting values: \[ W_{\text{ext}} = 2 \cdot 6.0 \times 10^{-6} \cdot 1.5 \times 10^3. \] Simplifying: \[ W_{\text{ext}} = 18 \, \text{mJ}. \]

Final Answer: The work done is 18 mJ.