An electric dipole with dipole moment $5 \times 10^{-6}\text{ C m}$ is aligned with the direction of a uniform electric field of magnitude $4 \times 10^5\text{ N/C}$. The dipole is then rotated through an angle of $60^\circ$ with respect to the electric field. The change in the potential energy of the dipole is:
A
0.8 J
B
1.0 J
C
1.2 J
D
1.5 J
The answer is B.
Solution
Change in potential energy is $\Delta U = -pE \cos 60^\circ - (-pE) = \frac{1}{2} pE = \frac{1}{2} (5 \times 10^{-6})(4 \times 10^5) = 1.0\text{ J}$.
The potential energy of an electric dipole in an external electric field is $U(\theta) = -p E \cos\theta$. Initially aligned: $\theta_1 = 0^\circ \implies U_1 = -pE \cos 0^\circ = -pE$. After rotating by $60^\circ$: $\theta_2 = 60^\circ \implies U_2 = -pE \cos 60^\circ = -\frac{1}{2} pE$. Change in potential energy: $\Delta U = U_2 - U_1 = -\frac{1}{2} pE - (-pE) = \frac{1}{2} pE$. Substituting the values: $\Delta U = \frac{1}{2} \times (5 \times 10^{-6}\text{ C m}) \times (4 \times 10^5\text{ N/C}) = \frac{2.0}{2} = 1.0\text{ J}$.
ConceptElectric Dipole Potential Energy
Electric Charges and Fields in past papers
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