#### 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?

#### 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, 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.

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Solution What is the Force Between Two Small Charged Spheres Concept: Forces Between Multiple Charges.