Question

Why must electrostatic field be normal to the surface at every point of a charged conductor ?

Answer 1

Lets assume that electric field lines are not normal to the surface of the conductor. So in this case field lines would be having a horizontal component which would make the charges displace in that direction.So work is said to be done as there is an electrostatic force due to electric field .But as the outer surface of the conductor is an equipotential surface so by its definition no work is done in moving a charge from one point to the other on it.

So W=|f||d| cos y=0 since F and d are non zero So cos y = 0 i.e. y=90

Thats why electric field lines have only a normal component.