Question

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

• A. The torque that $\overrightarrow{E}$ exerts on $\overrightarrow{p}$ is $(0.6\hat{i}-0.4\hat{j}-0.9\hat{k})Nm$
• B. The potential energy of the dipole is –0.6 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), (B)

The correct options are
A The torque that $\overrightarrow{E}$ exerts on $\overrightarrow{p}$ is $(0.6\hat{i}-0.4\hat{j}-0.9\hat{k})Nm$
B The potential energy of the dipole is –0.6 J.

Torque is given by,
$\overrightarrow{J}=\overrightarrow{P}\times \overrightarrow{E}$
$=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 3& 0\\ 3& 0& 2\end{array}\right|\times {10}^5\times {10}^{-6}$
$=(6\hat{i}-4\hat{j}-9\hat{k})\times {10}^{-1}$
$=(0.6\hat{i}-0.4\hat{j}-0.9\hat{k})N{m}^{-1}$
$U=-\overrightarrow{P}.\overrightarrow{E}$
$=-\left[2\right(3)+3(0)+(0\left)\right(2)\times {10}^5\times {10}^{-6}]$
$=-0.6J$
$U_{max}=PE$
$=\sqrt{2^2+3^2}\times \sqrt{9^2+4^2}\times {10}^{5-6}$
$=\sqrt{13}\times \sqrt{85}\times {10}^{-1}$
$=3.3J$