# What is the electric field and potential outside a spherical capacitor?

Two concentric spheres form a spherical capacitor with the same charges (but opposite signal). I know, by Gauss's law, that the electric field must be zero (actually, the flux must be zero, but I can't see how the flux can be zero and the electric field is not zero). But why there is no net field outside the spherical capacitor if the negative charges in the (for example) external sphere create a electric field in every direction - including de direction pointing to outside the sphere? (in this case, there is no other electric that could cancel it).

So I think it's supposed to be like in this picture - and the external electric is falling off with the distance, as any electric field, and the electric field of the charge inside makes it fall off faster - though it is never zero.

If it is so, why does Gauss's law says it is zero? If it's not, why? (in this latter case, how can we explain it NOT using Gauss's law, using only the charges and electric fields?) I suppose the same holds for cylindrical capacitors • The total charge is zero, so the electric field outside the shell is zero. If the center and the shell don't carry the opposite charge, then the field outside is not zero. – CuriousOne Aug 1 '16 at 23:27
• "But why there is no net field outside the spherical capacitor if the negative charges in the (for example) external sphere create a electric field in every direction - including de direction pointing to outside the sphere?" - Have you considered using superposition? – Alfred Centauri Aug 1 '16 at 23:31
• Alfred Centauri, yes I did and since the points outside the external sphere are closer to the the external sphere than the inside sphere, the "negative electric fiel" (electric field of the external sphere) is stronger than the "positive field" in the points outside the sphere. So the fields have the opposite directions and at first they could cancel each other but they don't because their magnitudes are different. – João Paulo Aug 1 '16 at 23:46
• CuriousOne, this is not true in general. The net charge in a dipole is zero though its electric field is not zero. Why would it be so with the shells? – João Paulo Aug 1 '16 at 23:49