# What is the force between two small charged spheres having charges

Question:

What is the force between two small charged spheres having charges of $2 \times 10^{-7} \mathrm{C}$ and $3 \times 10^{-7} \mathrm{C}$ placed $30 \mathrm{~cm}$ apart in air?

Solution:

Repulsive force of magnitude $6 \times 10^{-3} \mathrm{~N}$

Charge on the first sphere, $q_{1}=2 \times 10^{-7} \mathrm{C}$

Charge on the second sphere, $q_{2}=3 \times 10^{-7} \mathrm{C}$

Distance between the spheres, $r=30 \mathrm{~cm}=0.3 \mathrm{~m}$

Electrostatic force between the spheres is given by the relation,

$F=\frac{q_{1} q_{2}}{4 \pi \epsilon_{0} r^{2}}$

Where, $\epsilon_{0}=$ Permittivity of free space'

$\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \mathrm{Nm}^{2} \mathrm{C}^{-2}$

$F=\frac{9 \times 10^{9} \times 2 \times 10^{-7} \times 3 \times 10^{-7}}{(0.3)^{2}}=6 \times 10^{-3} \mathrm{~N}$

Hence, force between the two small charged spheres is $6 \times 10^{-3} \mathrm{~N}$. The charges are of same nature. Hence, force between them will be repulsive.