Question

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

Answer 1

The correct answer is: $6 × 10^{−3}N$
Repulsive force of magnitude $6 × 10^{−3} N$
Charge on the first sphere, $q_1$ $= 2 × 10^{−7} C$
Charge on the second sphere, $q_2 = 3 × 10^{−7} C$
Distance between the spheres, r = 30 cm = 0.3 m
Electrostatic force between the spheres is given by the relation
$F = \frac{1}{4πε_0}.\frac{q_1q_2}{r^2}$
Where, $ε_0$= Permittivity of free space and \frac{1}{4πε_0}$$= 9 × 10 ^9 Nm^2C^{-2}
Therefore, force
$F =\frac{9 × 10^ 9 ×\,10^{-7}}{ (0.3)^2} = 6 × 10^{-3} N$
Hence, force between the two small charged spheres is $6 × 10^{−3}N$. The charges are of same nature. Hence, force between them will be repulsive.