Question

The separation between the two charges $+q$ and $-q$ becomes double. The value of force will be:

• A. two fold
• B. half
• C. four fold
• D. one fourth

Answer 1

Answer: (D)

The force between two charges $q$ and $-q$ is
$F=\frac{1}{4\pi {\epsilon }_0}\frac{q\times -q}{r^2}=-\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{r^2}$
where $r=$ separation between the charges
$\therefore F^{\prime }=\frac{1}{4\pi {\epsilon }_0}\frac{q\times -q}{r^{\prime 2}}$
$=-\frac{1}{4\pi {\epsilon }_0}\times \frac{q}{(2r{)}^2}$
$\left(\because r^{\prime }=2r\right)$
$=\frac{1}{4}F$