Write Coulomb's law and explain its scalar form.

Explanation

The electric force between two point charges varied inversely as the square of the distance between the charges and was directly proportional to the product of the magnitude of the two charges and acted along the line joining the two charges.

Thus, if two point charges `q_(1), q_(2)` are separated by a distance r in vacuum, the magnitude of the force (F) between them is given by,
`F = (q_(1)q_(2))/r^(2)`
`therefore F = k(q_(1).q_(2))/r^(2)`
`therefore F = k(q_(1).q_(2))/r^(2)`....................(1)
where, fcis the proportionality constant also called Coulombian constant.
Experimentally it is found that `k = 8.9875 xx 10^9 Nm^2C^(-2)` . In general, it is taken as `k = 9 xx 10^9 Nm^2C^(-2)`.
`rArr K = 1/(4pi epsilon_(0))`
Where, `epsilon_(0)` = permittivity in free space
`=8.9 xx 10^(-12) C^(2) N^(-1)m^(-2)`
Hence, electric force is free space,
`F = 1/(4piepsilon_(0)) (q_(1)q_(2))/r^(2)`.......... (2)
If the charges are at distance V in any mediui instead of free space, then electric force i medium,
where, `epsilon` = permittivity in medium.
`rArr` Now, relartive permittivity `=e_(r) = epsilon/e_(00 = k` dielectric constant.
`rArr` By taking rato of equation (3) to (2)
`F_(m)/F = epsilon_(0)/epsilon = 1/k`
`therefore F_(m) = F/k`
Thus, electric force between two charges is `1/k` medium is 7- times the electric force in free k
space.