Question

A force of $40N$ is acting between two charges in air. If the space between them is filled with glass with ${\epsilon }_r=8$, what will be the force?

• A. 15 N
• B. 320 N
• C. 5 N
• D. 32 N

Answer 1

Answer: (C)

From Coulombs law the force between two charges is
$F=\frac{1}{4\pi {\epsilon }_{0}K}\cdot \frac{q_1{q}_2}{r^2}$
where $r$ is distance between the charges and $K$ the dielectric constant.
In air: $F_1=\frac{1}{4\pi {\epsilon }_{0}K}\cdot \frac{q_1{q}_2}{r^2}=40N$
In glass: $F_2=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{q_1{q}_2}{8r^2}$
$\therefore \frac{F_1}{F_2}=\frac{40}{F_2}=8$
$\Rightarrow F_2=5N$