Question

The charges on two spheres are $+7\mu C$ and $-5\mu C$ respectively. They experience a force $F$. If each of them is given an additional charge of $-2\mu C$, then the new force of attraction will be :

• A. $F$
• B. $\frac{F}{2}$
• C. $\frac{F}{\sqrt{3}}$
• D. $2F$

Answer 1

Answer: (A)

$F$

Given, $q_1=+7\mu C=+7\times {10}^{-6}C$
$q_2=-5\mu C=-5\times {10}^{-6}C$
New force $F^{\prime }=$?
We know that, $F=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{q_1{q}_2}{r^2}$
$F=\frac{1}{4\pi {\epsilon }_0}\frac{(+7\times {10}^{-6})(-5\times {10}^{-6})}{r^2}$
$=-\frac{1}{4\pi {\epsilon }_0}\frac{35\times {10}^{-12}}{r^2}N$
$F^{\prime }=\frac{1}{4\pi {\epsilon }_0}\frac{(+5\times {10}^{-6})(-7\times {10}^{-6})}{r^2}$
$=-\frac{1}{4\pi {\epsilon }_0}\frac{35\times {10}^{-12}}{r^2}N$
$\Rightarrow F^{\prime }=F$