Suppose a conducting spherical shell with a cavity inside it is placed in a uniform horizontal electric field. My question is: Will the electric field in the cavity be zero?
I understand that the electric field in the conducting region will be zero. Also from what I understand, due to electrostatic shielding, the charges/field outside the cavity do not affect the field inside the cavity, therefore, the field inside the cavity must be zero too. Is this correct?
In a conductor electrons are free to move. If they are acted on by a force, they will accelerate in the direction of the force. If a conductor is placed into an external electric field, a force F = -eE acts on each free electron. Electrons accelerate and gain velocity in a direction opposite to the field. Soon electrons will pile up on the surface on one side of the conductor, while the surface on the other side will be depleted of electrons and have a net positive charge. These separated negative and positive charges on opposing sides of the conductor produce their own electric field, which opposes the external field inside the conductor and modifies the field outside.
When enough electrons have piled up on one side and enough positive charge has been left on the other side, then the field produced by these separated charges exactly cancels the external field inside the conductor, and electrons inside the conductor no longer experience a force. This is the case in the picture shown above. The inside of the conducting sphere is field-free, while the previously constant external field outside has been modified.
This same exact thing happens on the surface of the cavity if there was an initial charge placed inside the cavity. The resulting fields cancel each other, and so it would be 0 inside. In the case where there are no charges inside the cavity, there is no question of a field, and again, your total field is 0.
Thus yes, you are absolutely correct in assuming the field inside would be 0.
