Question

Assertion$\left(A\right)$: If a dipole $\left(\overrightarrow{p_1}\right)$ is moved along the line normal to the axis (shown in dotted line) of another dipole $\left(\overrightarrow{p_2}\right),$ their interaction energy does not change.



Reason$\left(R\right)$: The electric field due to $\left(\overrightarrow{p_2}\right)$ at the position of $\left(\overrightarrow{p_1}\right)$ is normal to $\left(\overrightarrow{p_1}\right)$

Select the most appropriate answer from the options given below

• A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
• B. Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$
• C. $A$ is true but $R$ is false
• D. $A$ is false and $R$ is also false

Answer 1

The correct option is A Both $A$ and $R$ are true and $R$ is the correct explanation of $A$

Field due to $\left(\overrightarrow{p_2}\right)$ on $\left(\overrightarrow{p_1}\right)$ is,


$\therefore$ $\left(\overrightarrow{p_1}\right)\perp E_2,$
As we know, potential energy of a dipole is,

$U=-\overrightarrow{p}\cdot \overrightarrow{E}=pE\cos \theta$

Here, $\theta ={90}^{\circ }\Rightarrow U=0$

As the dipole$\left(\overrightarrow{p_1}\right)$ moves along the dotted line, direction of Field due to $\left(\overrightarrow{p_2}\right)$ on $\left(\overrightarrow{p_1}\right)$ remains perpendicular to $\left(\overrightarrow{p_1}\right)$
Hence interaction energy remains same.

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.