State Coulomb's law of force in electrostatics. Express it in vector form.

Explanation

Coulomb.s law. It states that two stationary electric point charges attract or repel each other with a force which is directly proportional to the product of magnitude of the charges and inversely proportional to the square of the distance between them.
COulomb.s law in vector form
Let `q_(1) and q_(2)` charges be separated by a distance r.

let `hatr_(12)`=unit vector pointing from `q_(1) ` to `q_(2)`
`hatr_(21)=` unit vector pointing from `q_(1)" to "q_(1)`
`vecF_(21)`=force exerted on `q_(2)" by " q_(2)`
Then `vecF_(12)=(1)/(4piepsi_(0))(q_(1)q_(2))/(r^(2))hatr_(21)` . . . (i)
and `vecF_(21)=(1)/(4piepsi_(0))(q_(1)q_(2))/(r^(2))hatr_(12)`
or `vecF_(21)=-(1)/(4piepsi_(0))(q_(1)q_(2))/(r^(2))hatr_(21)` . . . (ii)
Adding (i),(ii) we get
`vecF_(12)+vecF_(21)=0`
or `vecF_(12)=-vecF_(21)`
Definition of one coulomb
IN vaccum, `F=9xx10^(9)(q_(1)q_(2))/(r^(2))`
If `q_(1)=q_(2)=q(say),r=1m,F=9xx10^(9)N`
Then, `9xx10^(9)=9xx10^(9)*(q*q)/(1)`
or `q=pm1C`
`therefore` One coulomb is charge which when placed before an equal and similar charge in vacuum at 1m, repels with a force of `9xx10^(9)N`.