A neutral conductor completely encloses a hole inside of it. You observe the outer surface of this conductor carries a charge of -12 uC. (a) Can you conclude that there is a charge inside the hole? If so, what is the charge? (b) How much charge is on the inner surface of the conductor?

ok there wouldn't be any charge on the outside correct? so if there isn't any charge on the inside, but there is charge on the inner surface of the conductor right? I am confused!

a) They already said that there IS an outer surface charge, and they told you what it is. Its value equals that of the charge inside the hole. That is necessary to make the charge inside the conductor zero, according to Gauss' Law.

b) There is an inner surface charge also. It is the opposite of the charge inside the hole, since there can be no E-field between the two surfaces of the conductor

It is possible to conclude that there is a charge inside the hole of the conductor based on the information provided. In this case, since the outer surface of the conductor carries a charge of -12 uC, this indicates that there must be an equal and opposite charge inside the conductor.

To determine the charge inside the hole, we can use the principle of charge conservation. Since the net charge of the conductor is zero (neutral), the charge inside the hole must be +12 uC to balance out the -12 uC charge on the outer surface.

Regarding the charge on the inner surface of the conductor, since the conductor is neutral overall, the inner surface would also carry a charge of -12 uC, cancelling out the charge on the outer surface. This is because a conductor in electrostatic equilibrium distributes charge evenly on its surfaces.

So, in summary:
(a) The charge inside the hole is +12 uC.
(b) The charge on the inner surface of the conductor is -12 uC.

To determine whether there is a charge inside the hole, we need to understand how charges distribute themselves in a conductor and how that affects the electric field inside the conductor.

When a conductor is in electrostatic equilibrium, the charges in the conductor will redistribute themselves such that the electric field inside the conductor is zero. This means that all excess charge resides on the outer surface of the conductor, and the inner volume of the conductor is electrically neutral.

Given that the outer surface of the conductor carries a charge of -12 uC, we can conclude that there must be an equal amount of positive charge inside the conductor to balance out the negative charge on the outside. Therefore, there is a charge in the hole, and its magnitude is also 12 uC.

As for the charge on the inner surface of the conductor, it will be equal in magnitude and opposite in sign to the charge inside the hole. So the charge on the inner surface will also be 12 uC, but with a positive sign.

To summarize:
(a) Yes, there is a charge inside the hole, and its magnitude is 12 uC.
(b) The charge on the inner surface of the conductor is 12 uC with a positive sign.