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.