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As per this diagram a point charge $+q$ is placed at the origin $O$. Work done in taking another point charge $-Q$ from the point $A$ [coordinates $(0, a)]$ to another point $B[\operatorname{coordinates}(a, 0)]$ along the straight path $A B$ is
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The correct answer is:
ZERO
The work done in carrying a test charge consists in product of difference of potentials at points $A$ and $B$ and value of test charge.
Potential at A
$V_A=\frac{1}{4 \pi \varepsilon_0} \frac{q}{a}$
Potential at B
$V_B=\frac{1}{4 \pi \varepsilon_0} \frac{q}{a}$
Thus, work done in carrying a test charge $-Q$ from $A$ to $B$
$W=\left(V_A-V_B\right)(-Q)=0$
Potential at A
$V_A=\frac{1}{4 \pi \varepsilon_0} \frac{q}{a}$
Potential at B
$V_B=\frac{1}{4 \pi \varepsilon_0} \frac{q}{a}$
Thus, work done in carrying a test charge $-Q$ from $A$ to $B$
$W=\left(V_A-V_B\right)(-Q)=0$
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