Question

Figure shows three circular arcs, each of radius $R$ and charges $+Q,-2Q$ and $3Q$ are present in respective arcs.


The net electric potential at the centre of curvature is

• A. $\frac{2kQ}{R}$
• B. $\frac{8kQ}{R}$
• C. $\frac{kQ}{R}$
• D. $\frac{kQ}{2R}$

Answer 1

The correct option is A $\frac{2kQ}{R}$

Let the potential at centre of arc due to charge $Q,-2Q$ and $3Q$ is $V_1,V_2$ and $V_3$ respectively

The net potential at centre is algebraic sum of potential due to all the charges.
$V=V_1+V_2+V_3$

$V=\frac{kQ}{R}+\frac{-2kQ}{R}+\frac{3kQ}{R}$$=\frac{2kQ}{R}$

$\begin{array}{c}\text{Why this question ?}\\ \text{Potential is a scalar quantity and can}\\ \text{be added or subtracted algebraically.}\end{array}$