Question

The above figure shows the variation of potential $V$ or electric field with $r$ for a point charge $Q$. Which of the given curves represent $E$ versus $r$ or $V$ versus $r$ ?

• A. $I \rightarrow E$ versus $r, II \rightarrow V$ versus $r$
• B. $I \rightarrow V$ versus $r, II \rightarrow V$ versus $r$
• C. Both represent $E$ versus $r$
• D. None of the above

Answer 1

Answer: (A)

$E=\frac{K Q}{r^{2}}$
$\Rightarrow E \propto \frac{1}{r^{2}}$
$\Rightarrow V=\frac{K Q}{r}$
$\Rightarrow V \propto \frac{1}{r}$
So, for $0 < r < 1$, the curve $E$ will be above $V$ and for $r>1$, the curve $E$ will be below $V$ at $r=1, E=V$