Charge inside a spherical conducting shell

[zeeva]

If a charge is placed inside a spherical conducting shell, is the total electric field inside it zero? I am thinking that if the charge is positive, then the conducting shell will have an equal amount of negative charge on its inner surface, therefore the E field should be zero inside, right?

[diazona]

You mean the electric field in the space filled by the conducting material? In that case you're right, it would be zero. That's pretty general, actually: any space filled with conducting material will have zero electric field, because if the electric field were nonzero, it would push around electrons inside the conductor until they canceled out the external field.

Of course the E field in the empty space inside the shell would not be zero.

[zeeva]

Does that mean that if the shell had a hole through it and we wanted to move the charge from the inner radius to the outer radius, the work would be zero?

[Anamitra]

It would be better to use energy considerations here. The value of potential energy would be different in the initial and the final configurations.

Work done=Change in Potential Energy

[diazona]

Does that mean that if the shell had a hole through it and we wanted to move the charge from the inner radius to the outer radius, the work would be zero?
Not if you move the charge through the hole. The space of the hole is not filled with conducting material, so there's no reason the electric field inside it would be zero.

Of course, if you move the charge through the metal itself, and not through the hole, then the work done would be zero.