Question

Which of the following graph of electrostatic force between two positive charges $\left(F_e\right)$ vs $r^2$, is a correct representation?
($r$ is the distance between two charges)

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

From Coulomb's law,

$F_e=\frac{k{q}_1{q}_2}{r^2}$

So, we can say that electrostatic force between two charges is an inverse square function.

i.e. $F_e\propto \frac{1}{r^2}$

$\Rightarrow F_e=\frac{\text{constant}}{r^2}$

If $r^2\uparrow \to F_e\downarrow$
and when, $r\to 0,F_e\to \infty$

For a given pair of charge at certain separation,

$F_e{r}^2=k{q}_1{q}_2=\text{constant}$

This resembles $xy=\text{constant}$

So, graph of $F_e$ vs $r^2$ will be rectangular hyperbola.

Hence, option $\left(c\right)$ is correct.

$\begin{array}{c}\text{Why this question ?}\\ \text{Tip: In graph of}{F}_e\text{vs r or}{F}_e\text{vs}{r}^2\\ r=0\text{and}r=\infty \text{are the asymptotes for the hyperbola.}\end{array}$