Question

Two points charges placed at a distance r, in the air experience a certain force, then the distance at which they will experience the same force in the medium off dielectric constant K is

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

Answer 1

Answer: (C)

$\frac{r}{\sqrt{K}}$

Let 2 charges $q_{11}{1}_2$

$F=\frac{k^1{q}_1{q}_2}{r^2}\left(k^1=\frac{1}{4\pi \in o}\right)$

Now both $q_1{q}_2$ ARE PLACED IN DIELUTRIC MEDIUM OF k

$\begin{array}{c}\frac{k^1{q}_1{q}_2}{r^2}=\frac{K^1{q}_1{q}_2}{K{r}_1^2}\Rightarrow \frac{1}{r^2}=\frac{1}{r_1^{2}K}\\ \Rightarrow r_1=\frac{r}{\sqrt{K}}\end{array}$