Question

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

Answer 1

This, like many other things in electricity in magnetism, is a consequence of symmetry! See how the forces on the test charge are all slanted the same way towards it? The left and right components of the forces will cancel out but leave the outward normal force leftover. See how the x-components cancel each other out and will only leave the outwards force? =)