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Numerical

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?

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#### Solution

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=(q_1q_2)/(4piin_0r^2)`

Where, ∈_{0} = Permittivity of free space

`1/(4piin_0)=9xx10^9 Nm^2C^-2`

`F=(9xx10^9xx2xx10^-7xx3xx10^-7)/((0.3)^2)=6xx10^-3N`

Hence, the force between the two small charged spheres is 6 × 10^{−3} N. The charges are of the same nature. Hence, the force between them will be repulsive.

Concept: Superposition Principle - Forces Between Multiple Charges

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