What is the force between two small charged spheres having charges of `2xx10^(-7)C and 3xx10^(-7) C` placed 30cm apart in air ?

Options

A. `6 xx 10^(−4)` N
B. `6 xx 10^(−3)` N
C. `6 xx 10^(−6)` N
D. `5 xx 10^(−3)` N

Answer

B

Explanation

Repulsive force of magnitude `6 xx 10^(−3) N`
Charge on the first sphere, `q_(1) = 2 xx 10^(−7) C`
Charge on the second sphere, `q_(2) = 3 xx 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_(1)q_(2))/(4 piepsilon_(0) r^(2))`
Where, ` epsilon_(0)` = Permittivity of free space
`(1)/((4 piepsilon_(0)) = 9 xx 10^(9) Nm^(2) C^(-2)`
`F = (9 xx 10^(9) xx 2 xx 10^(-7) xx 3 xx 10^(-7))/((0.3)^(2)) = 6 xx 10^(-3)N`
Hence, force between the two small charged spheres is `6 xx 10^(−3)` N. The charges are of same nature. Hence, force between them will be repulsive.