Question

Two equal charges placed in air and separated by a distance of $2m$ repel each other with a force of ${10}^{-4}kgf$. Calculate the magnitude of either of the charges.

Answer 1

Let each charge be $q$.

Using Coulomb's Law,

$F=\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{r^2}$

Here, $r=2m$

$F={10}^{-4}\times 9.8N$

$={10}^{-4}\times 10N$

$q^2=F\times 4\pi {\epsilon }_0\times r^2$

$={10}^{-4}\times \frac{10\times 1}{9\times {10}^9}\times (2{)}^2$

$=\frac{{10}^{-12}}{9}\times (2{)}^2$

So, $q=\frac{2}{3}\times {10}^{-6}$

$=0.66\mu C$

Each charge is $0.66\mu C$