# Charge inside a charged hollow conducting sphere with a hole

How are the following results theoretically explained?

As part of an electrostatics exercise we were to measure the charge on the outside and inside surfaces of a charged hollow conducting sphere with a ~2cm radius hole on the top.

The outside surface of the sphere was connected to a positive charge generator.

I used an electrometer and a probe to measure the charge density of the respective surfaces.

The result of the measurements confused me: 25V when probing the outside surface and 33V on the inside surface. What's more, my professor found ~10V on the inside as well (not sure about the exact value).

According to Gauss' law, there shouldn't be any charge on the inner surface of an externally charged conductor, so how were the measurements possible?

Additional parameters that might give a clearer picture:

• I was not electrically grounded as I was probing.
• The inside surface opposite the hole has an inwards bump for a screw to secure the sphere to a rod below it.
• The probe touched a grounded Faraday cage before each probing.

I take it that any inductive charging of the probe should have been somewhat mitigated as the probe entered and left the sphere, albeit the electrometer was not quite far from it.

The imperfectness of the inside surface should not have an effect on the existence of charge on its inside surface.

The existence of the hole on the top should be accounted for by a higher charge density around the edges of the hole.

With all of my assumptions in mind, which one is wrong or missing so that these measurements are possible?

This post is related (and seemingly unanswered) and so is this video.

• Volts is not a measurement of charge. It is a measurement of potential difference. The question is, what 2 things were you measuring the potential difference between, and was it the same 2 things in all 3 cases? The potential on the outer and inner surfaces should be the same for a conductor. It is not clear what equipment you were using, nor how you were using it. Probably you were not using it correctly. – sammy gerbil Jan 7 at 4:12
• Yes, it should be clear to everyone that charge is not measured in volts. I stated that I used an electrometer; meaning it was connected to two cylindrical meshes (one was inside the other being shielded from outside effects). The outside mesh was grounded and acted like a Faraday cage. I would place charge on the inside mesh and read the electrometer. – Nikola Petrovic Jan 7 at 8:29
• I did not state that I used an electrometer on the sphere itself, as that would achieve nothing and not allow me to measure the existence of charge or relative charge density. – Nikola Petrovic Jan 7 at 8:46