Question

The ratio of forces between two point charges in the two cases when their separation is halved and when it is doubled, is

• A. 1 : 2
• B. 4 :1
• C. 8 : 1
• D. 16 : 1

Answer 1

Answer: (D)

According to Coulomb's law
$F=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r^2}$
For same medium and charges, $F\propto \frac{1}{r^2}$
So, $\frac{F_1}{F_2}=\frac{r_2^2}{r_1^2}$
Here, $r_1=\frac{r}{2}$ and $r_2=2r$
$\therefore \frac{F_1}{F_2}=\frac{{\left(2r\right)}^2}{{\left(\frac{r}{2}\right)}^2}=16$