Q.An electric dipole consists of two unlike charges of magnitude 2×10⁻⁶ C each and separated by 4 cm. The dipole is placed in an external electric field of 10⁵ N/C. Calculate the work done by an external agent to turn the dipole through 180°.

Work done to rotate a dipole from aligned ($0°$) to anti-aligned ($180°$) with the field is $W=2pE$; substituting the numbers gives 0.016 J.

Dipole moment:

$p = q \times d = (2\times10^{-6}\ \text{C})(0.04\ \text{m}) = 8\times10^{-8}\ \text{C·m}$

Work done by an external agent to rotate a dipole from angle $\theta_1$ to $\theta_2$ (measured from the field direction) in a uniform field $E$:

$W = pE(\cos\theta_1 - \cos\theta_2)$

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