Final answer:
The statement about metal not being in equilibrium with a zero net electric field is false. In electrostatic equilibrium, the free electrons in the metal will arrange themselves to cancel out any applied electric fields, resulting in a zero net electric field within the conductor.
Step-by-step explanation:
The statement that a metal not being in equilibrium if the net electric field at a particular location inside it is zero is false. In the case of a conductor, like metal, in electrostatic equilibrium, the net electric field inside the conductor must be zero. This is because the free electrons within the metal will arrange themselves such that they cancel out any applied electric fields resulting in an electric field of zero inside the conductor.
For example, consider a cavity within a metal that has an excess charge. The metal will redistribute charges such that the net electric field inside the cavity is zero. Similarly, if a charged object is placed near a conductor, polarization occurs, and charges within the conductor rearrange themselves until the electric field inside the conductor is null.
To illustrate further, think of the analogy where a bar magnet is dropped through a copper tube. When falling through the tube, the bar magnet induces an electric current in the tube due to the changing magnetic field, verifying the principle of induction and the movement of charges in response to fields. This does not alter the requirement that the net electric field inside the conductor must be zero in electrostatic equilibrium. The application of this principle is consistent with the observed behaviors of charges in conductive materials regardless of the external influences, as long as static conditions are maintained.