Question

Two small dipoles of dipole moment $P_1$ and $P_2$ are placed as shown in figure. $k=\frac{1}{4\pi {ϵ}_o}$

• A. Torque on $P_2$ due to $P_1$ is zero
• B. Torque on $P_1$ due to $P_2$ is $\frac{2k{P}_1{P}_2}{r^3}$
• C. Torque on $P_1$ due to $P_2$ is zero
• D. Force on $P_1$ due to $P_2$ is zero

Answer 1

Answer: (B), (D)

The correct options are
B Torque on $P_1$ due to $P_2$ is $\frac{2k{P}_1{P}_2}{r^3}$
D Force on $P_1$ due to $P_2$ is zero


$\overrightarrow{E_1}$ is field at $\overrightarrow{P_2}$ due to $\overrightarrow{P_1}$
$\overrightarrow{E_2}$ is field at $\overrightarrow{P_1}$ due to $\overrightarrow{P_2}$
$E_1=\frac{k{P}_1}{r^3}$ and $E_2=\frac{2k{P}_2}{r^3}$
$\overrightarrow{\tau }=\overrightarrow{P}\times \overrightarrow{E}$
So $\Rightarrow |\overrightarrow{\tau }|=P_1{E}_2\text{sin}{90}^o=\frac{2k{P}_1{P}_2}{r^3}$
Force $F=-\frac{\partial U}{\partial r}$ where $U=-PE\text{cos}\theta$
here $\theta =\frac{\pi }{2}$, U = 0 and F = 0.