Question: Q. 1. A point charge $Q$ is placed at point ’ $O$ ’ as shown in figure. Is the potential at point $A$, i.e., $V_{A^{\prime}}$ greater, smaller or equal to potential, $V_{B}$ at point $B$, when $Q$ is (i) positive, and (ii) negative charge?
U] [Foreign I, II, III 2017]
$$ O \bullet \quad A \bullet \quad B \bullet $$
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Solution:
Ans. (i) $V_{A}>V_{B}$ $1 / 2$ (ii) $V_{A}<V_{B}$
[CBSE Marking Scheme 2017]
Detailed Answer :
Let $r_{A}$ is the distance of point $A$ from point charge $Q$ and $r_{B}$ is the distance of point $B$ from point charge $Q$.
Potential at point $A$ :
$$ V\left(r_{A}\right)=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q}{r_{A}} $$
Potential at point $B$ :
$$ V\left(r_{B}\right)=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q}{r_{B}} $$
Since $r_{A}<r_{B}$, so when :
charge $Q$ is positive; $V_{A}>V_{B}$
charge $Q$ is negative; $V_{A}<V_{B}$
