Question

Two point charges placed at a distance ${}^{\prime }{r}^{\prime }$ in air exert a force ${}^{\prime }{F}^{\prime }$. The distance at which they exert same force when placed in a certain medium (dielectric constant $K$) is

• A. $rK$
• B. $\frac{r}{K}$
• C. $\frac{r}{\sqrt{K}}$
• D. $r\sqrt{K}$

Answer 1

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

Electrostatic force in vacuum is given as

$F=\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_2}{r^2}....\left(1\right)\text{Electrostatic force in dielectric medium is}{F}^{\prime }=\frac{1}{4\pi {ϵ}_{0}K}\frac{q_1{q}_2}{r^{\prime 2}}.....\left(2\right)$

According to the question exerted force is same

So,
$F^{\prime }=F$

Or,
$\frac{1}{4\pi {ϵ}_{0}K}\frac{q_1{q}_2}{r^{\prime 2}}=\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_2}{r^2}$

After solving
$r^{\prime }=\frac{r}{\sqrt{k}}$

Distance at which they exert same force is $\frac{r}{\sqrt{k}}$