Question

An electric dipole moment $\overrightarrow{P}=(2.0\hat{i}+3.0\hat{j})\mu$ is placed in a uniform electric field $\overrightarrow{E}=(3.0\hat{i}+2.0\hat{k})\times {10}^{5}N{C}^{-1}$ .

• A. The torque that $\overrightarrow{E}$ exerts on P is $(0.6\hat{i}-0.4\hat{j}-0.9\hat{k})$ Nm
• B. The potential energy of the dipole is 0.9 J
• C. The potential energy of the dipole is 0.6 J
• D. If the dipole is rotated in the electric field, the maximum potential energy of the dipole is 1.3 J

Answer 1

Answer: (A), (C), (D)

The torque that $\overrightarrow{E}$ exerts on P is $(0.6\hat{i}-0.4\hat{j}-0.9\hat{k})$ Nm
If the dipole is rotated in the electric field, the maximum potential energy of the dipole is 1.3 J
The potential energy of the dipole is 0.6 J

Torque $\tau =\overrightarrow{P}\times \overrightarrow{E}=(2.0\hat{i}+3.0\hat{j}){10}^{-6}\times (3\hat{i}+2\hat{k}){10}^5=-0.9\hat{k}-0.4\hat{j}+0.6\hat{i}$

Potential energy $|U|=|-\overrightarrow{P}.\overrightarrow{E}|=0.6J$

If the dipole is rotated in field direction so for maximum potential

$U_{max}=|\overrightarrow{P}||\overrightarrow{E}|cos0=\sqrt{2^2+3^2}\times {10}^{-6}\times \sqrt{3^2+2^2}\times {10}^5=1.3J$