Where ε0 is the permittivity of free space and er is the radial unit vector. If you don't understand the math (you will one day), it means the electric field strength declines the further away you are from an electric source. If you are driving on a highway and notice a radio station fading, for example, it's because you are getting further away from the big radio transmitter tower.
The take-home is that this law gives us the foundation for a mathematical relationship that relates charge and electric fields within a fixed volume of space. A Faraday cage encloses such a fixed volume of space, and, if the cage is made of conductive material, the cage's defining characteristic is that it prevents external charges from inducing electric fields within that volume. Here are two of the main rules that govern this barrier effect:
1.Coulomb's Law demands that the charges in a conductor at equilibrium be as far apart as possible, and thus the net electric charge of a conductor resides entirely on its surface.
2.Any net electric field inside the conductor would cause charge to move since it is abundant and mobile, but equilibrium demands that the net force within the conductor is equal to zero. Thus, the electric field inside of the conductor is zero.
Rule 2 tells us that the electric field inside the conductor at equilibrium is zero, and Rule 1 tells us that the charge of the conductor will be found entirely at the surface (boundary). In other words, the surface of the conducting volume becomes a barrier where charges move to and around the surface to generate fields exactly opposing any charge that seeks to cross the border, thus maintaining an interior free from external electrical interference.