Why is the electric field perpendicular to the surface of a conductor?
Answers
If a vector, say a force vector, is making an angle of theta with the surface of an object, then that force will have a perpendicular component Fsin thetha and a tangential or parallel component (parallel to the surface) F cos theta.
These forces will try to accelerate the particles along and perpendicular and tangential directions with respect to the ground.
Now coming back to your question. If a field like is making an angle theta with the surface of a charged conductor, then that field line will try to accelerate the local charge (the charges present on the surface near that field line) tangentially as well as perpendicularly.
Now the charge cannot get accelerated perpendicularly as other forces will try to pull it back and cancel the forces out.
However the tangential component would accelerate the charges and that would make them move through the conductor. But in electrostatics, charges are supposed to be at rest.
Thus we conclude that eventually when electrostatic conditions have reached, the field lines must be perpendicular to the surface everywhere.
Hope this will help you (^_^)
If the electric field is not perpendicular to the surface of the conductor then it will have a component tangential to its surface which will cause flow charge carriers i.e,electrons which will give rise to surface currents but no such currents exist under static conditions
Therefore electric field is always perpendicular to the surface of the conductor
I hope it helps