I need some help with these questions.
Why is there no electric field at the center of a charged spherical conductor?
Does an electric field exist within a charged spherical conductor at points other than its center?
2 answers
There is no electric field inside conductors, not at the center, or anywhere else. Charges repel, and go to the surface.
It is important to note here that the reason why there is no field inside the conductor is simply due the fact that charges repel. However, the reason why the charges go to the surface is due to the inverse square Coulomb law.
Also, the fact that the electric field at the center of a spherical hollow conductor is zero only depends on the symmetry, not on Coulomb's law. But the fact that the electric field away from the center is zero does depend on Coulomb's law.
This fact has been used to test Coulomb's law, see here:
http://prola.aps.org/abstract/PRL/v26/i12/p721_1
Also, the fact that the electric field at the center of a spherical hollow conductor is zero only depends on the symmetry, not on Coulomb's law. But the fact that the electric field away from the center is zero does depend on Coulomb's law.
This fact has been used to test Coulomb's law, see here:
http://prola.aps.org/abstract/PRL/v26/i12/p721_1