Question

why is the electric field outside a spherical capacitor is zero??also why is potential on the external sphere which is earthed is zero??

Answer 1

Actually if we see the potential out side any charged spherical shell is given by $\frac{q}{4{\mathrm{\pi \epsilon }}_0\mathrm{r}}$, where r is the distance from centre of the sphere and q is the total charge. Now since the charge of the both sphere are same but with negative sign. Also the centre of the both of the sphere are same. So the distance of any point from the centre will also be same. So the potential become equal but with opposite sign. So total potential out side the sphere will be zero.

Now we consider the surface of the earth is at zero potential. Now if we connect any conducting surface to earth with resistance less wire the surface will become zero potential. This is because all connected conducting surface will be in equal potential. That's why outer surface with is connected to the earth will be in zero potential.