Question 705: Electrostats & Capacitance

Question

An electric dipole of dipole moment $6 	imes 10^{-6} \mathrm{Cm}$ is placed in uniform electric field of magnitude $10^{6} \mathrm{V} / \mathrm{m}$. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be _______ J.

Accepted Answer

Given values:
The dipole moment is $ p = 6 	imes 10^{-6} \ \mathrm{Cm} $.
The electric field is $ E = 10^6 \ \mathrm{V/m} $.
Formula for work done:
Work required to rotate the dipole is

$ W = \Delta U = -pE(\cos 	heta_f - \cos 	heta_i) $

where $ 	heta_i $ is the initial angle between the dipole and the electric field, and $ 	heta_f $ is the final angle.
Angles:
At the start, the dipole is parallel to the field ($ 	heta_i = 0^\circ $), so $\cos 	heta_i = 1$.
At the end, the dipole is opposite the field ($ 	heta_f = 180^\circ $), so $\cos 	heta_f = -1$.
Calculation:
$ W = -pE (\cos 180^\circ - \cos 0^\circ) = -pE(-1 - 1) = 2pE $
Plug in the values:
$ W = 2 	imes (6 	imes 10^{-6}) 	imes (10^6) = 2 	imes 6 = 12\ \mathrm{J} $

Electrostats & Capacitance

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