Practical considerations: I used a "Faraday Ice Pail" with the center "pail" removed for my cage. I placed the aluminum foil on a soft, squishy material like bubble-plastic so good contact could between the wire mesh "bowl" and the foil.

The concept here, related to Gauss's Law, is that the electric field will not penetrate into the inside of a conductor. If there is no charge enclosed, then there is no charge on the INSIDE of the conducting surface and therefore the electric field is ZERO on the inside of the conducting surface with no electric field within the confines of the conductor. The electric field lines from the radio transmitter will terminate on the conductor (or the mesh in this case) but not penetrate into them. Why it works with a mesh as coarse as the one here is due to the wavelength of the radio waves. We'll discuss this later in the semester. It is not necessary to ground the mesh since even ungrounded, Gauss's Law says that there will be no electric field inside a conductor, nor penetrating into a cavity contained inside a conductor.

This effect, called the "Faraday Cage Effect" is why cars usually have radio antennas that are outside the sheet metal skin of the car or imbedded into the windshield, or why it's hard to listen to a pocket radio inside a school bus with small windows, or listen to a radio inside a building with metal walls. If your house were made of metal studs and metal walls instead of wood and plaster, you would not be able to listen to radio without an outside antenna.

See also Gauss's Law: Flying Pie Tins.