An electric dipole with dipole moment 5×10^-6 C m is aligned with the direction of a uniform electric field of magnitude 4×10^5 N…

Question

An electric dipole with dipole moment 5×10^-6 C m is aligned with the direction of a uniform electric field of magnitude 4×10^5 N/C. The dipole is then rotated through an angle of 60^ with respect to the electric field. The change in the potential energy of the dipole is:

1. A. 0.8 J
2. B. 1.0 J (Correct answer)
3. C. 1.2 J
4. D. 1.5 J

Correct Answer

Option B — 1.0 J

Detailed Solution & Explanation

The correct answer is 1.0 J.

Key Points

• Potential energy of a dipole: $U=-PE\cos\theta$, so $\Delta U=PE(\cos\theta_i-\cos\theta_f)$.
• Here $\theta_i=0^\circ$, $\theta_f=60^\circ$: $\Delta U=PE\left(1-\dfrac{1}{2}\right)=\dfrac{PE}{2}$.
• $\Delta U=\dfrac{1}{2}\times 5\times10^{-6}\times 4\times10^{5}=1.0$ J.