Derive an expression for electric field intensity at a distance r from a point charge q.

Explanation

The electric field intensity due to a source charge at any point in the electric field is defined as the force experienced by a unit positive charge placed at that point.
Physical significance of electric field : The concept of electric, field helps us to understand the mechanism by which two charges kept at a distance exert force an each other.
Also as an alternative to Coulomb.s law, it gives a method to find the force experienced by one charge due to the other in terms of electric field produced by it.
Electric field intensity due to a point charge : Let a charge + Q be lying at origin O. Let `q_0` be the test charge placed in free space at a distance r from O in the electric field of charge Q.

According to Coulomb.s law, the force experienced by charge `q_0` is given by
`vecF = 1/(4pi in_0) (Qq_0)/(|vecr|^2) vecr`
where `vecr` is unit vector directed along OP.
Now electric field at P due to point charge Q is given by
`vecE = Lt_(q_0 to 0) (vecF)/(q_0) = 1/(4pi in_0) (Qq_0)/(q_0|vecr|^2)`
`vecE = 1/(4pi in_0) Q/(|vecr|^2) vecr`
which is the expression for electric field due to point charge at a distance r from charge Q.