design of a spherical capacitor?

Answer 1

You didn't describe any applications, however a simple "Christmas ornament" that was metallized both on the inside of the glass sphere and on the outside (with conductors connected) would serve as a spherical capacitor. You must have some reason for wanting a capacitor in this shape.

A transmission electron microscope utilizes the spherical properties of the vacuum chamber to be able to visualize individual atoms. It operates as a 'spherical capacitor' until the voltage is raised enough to start viewing the individual atoms.

If you wanted to operate at high frequencies there are series resistance factors you need to take into consideration. You might be able to use it as a measuring sensor under the right conditions.

Answer 2

Tough structure but think of a tootsie roll pop where the chocolate is one electrode, the hard candy is the other and there's an insulator between them with a contact to each electrode.

Answer 3

Here's some helpful links.