Derive an expression for electric field intensity at a point due to a point charge.

Explanation

Consider a point where we want to find the electric field intensity due to point charge +placed at a point O.
Imagine a small positive test charge go at P. Join OP. Let `OP=r`.
According to Coulomb.s law, force on the charge at P is
`vecF=1/(4pivarepsilon_(0))(qq_(0))/r^(2)hatr`
`" "impliesvec(F)/q_(0)=1/(4 pivarepsilon_(0))q/r^(2)hatr`
But,`" "vec(F)/q_(0)=vec(E)(at P)" ":." "vec(E)=1/(4pivarepsilon_(0))q/r^(2)hat(r)`
The direction of `vec(E)` is along the line joining the two charges. Also `vec(E)` is directed away from the point charge, if the point charge is positive and if the point charge is negative then E is directed towards the point charge.