why is there no electric field at the center of a charged spherical conductor?
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because all of the charged particles are at the edge
this is because for charged conductors the net electric field is always perpendicular to the surface area and parallel to surface area vector. so it is always outwards and that is why the electric field at center of charged spherical conductor is zero
adding to what rajesh said-
if the net electric field wasn't always perpendicular to the surface and was instead tangential or at some angle, then it would lead to surface currents. Which implies that if you leave an uncharged body in an external electric field then it would automatically start producing currents.
That is obviously against the Law of Conservation of Charges and of course hysterical.