Question

The electrostatic force on a metal sphere of charge $0.4$ $\mu$C due to another identical metal sphere of charge $-0.8$ $\mu$C in air is $0.2$N. Find the distance between the two spheres and also the force between the same two spheres when they are brought into contact and then replaced in their initial positions.

Answer 1

Given two identical spheres having charges: $q_1=0.44C$

$q_2=-0.84C$

Force between them, $F=0.2N$

i) To find distance between then two spheres:

We use Coulomb's Law, $F=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r^2}$

$r^2=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{F}=\frac{9\times {10}^9\times 0.4\times 0.8\times {10}^{-12}}{0.2}$

$=14.4\times {10}^{-3}$

$=144\times {10}^{-4}$

So, $r=12\times {10}^{-2}m$

where, $r=$ distance of separation between two spheres.

ii) We have to find force between same two spheres when brought in contact and placed at same positions.

So, when the two spheres are brought in contact; charge on each sphere is $Q=\frac{0.4+0.8}{2}\mu C=0.6\mu C$

So, now force is $=\frac{1}{4\pi {\epsilon }_0}\frac{Q^2}{r^2}$

$=\frac{9\times {10}^9\times (0.6\times {10}^{-6}{)}^2}{144\times {10}^{-4}}$

$=\frac{9\times {10}^9\times 0.36\times {10}^{-12}}{144\times {10}^{-4}}$

$=0.0225\times 10=0.225N$