Question

The electric field in a region surrounding the origin is uniform and along $x-$ axis. A small circle is drawn with the centre at origin and cutting the axes at points $\text{A, B, C}$ and $\text{D}$ having coordinates $(a,0),(0,a),(-a,0)$ and $(0,-a)$ respectively. Then the potential energy for a test charge $q$ placed at these position will be minimum at:

• A. $\text{A}$
• B. $\text{B}$
• C. $\text{C}$
• D. $\text{D}$

Answer 1

The correct option is A $\text{A}$


The points $\text{A, B, C}$ and $\text{D}$ have been shown in the above figure.
The dotted lines are equally spaced equipotential surfaces.

$\Rightarrow$ The points $\text{B}$ and $\text{D}$ are situated on the diameter of the circle, which is an equipotential surface.

$\therefore V_B=V_D$

Also, potential decreases in the direction of electric field $\overrightarrow{E}$.

$\Rightarrow V_C>V_B=V_D>V_A$

And P.E for a charge is $U=qV$

Hence, $U_{min}$ will be for position $\text{A}$, because $V$ is minimum at $\text{A}$.