Question

Two point charges placed at a certain distance r in air exert a force F on each other. The distance r' at which these charges will exert the same force in medium if dielectric constant k is given by

• A. r
• B. $\frac{r}{k}$
• C. $\frac{r}{\sqrt{k}}$
• D. none of these

Answer 1

The correct option is C $\frac{r}{\sqrt{k}}$

Two point charge placed at a certain distance $=r$

force $=F$

dielectric constant $=k$

Let, two point charges $q_1$ and $q_2$ are separated $r$ distance from each other.

Then, force experienced between then,

$F=\frac{q_1{q}_2}{4\pi {ϵ}_0{r}^2}$

Put, $F=\frac{q_1{q}_2}{4\pi {ϵ}_0{r}^2}$

$\therefore$ $\frac{4q_1{q}_2}{4\pi {ϵ}_0{r}^2}=\frac{q_1{q}_2}{k\left(4\pi {ϵ}_0{r}^2\right)}$

$\Rightarrow \frac{1}{r^2}=\frac{1}{4r^{2}h}$

$\Rightarrow \frac{1}{r^2}=\frac{1}{{kr}^2}$

taking square root both sides

$\frac{1}{r}-\frac{1}{\sqrt{k}{r}^1}$

or, $r^1=\frac{r}{\sqrt{k}}$