Faraday cage

An employee of the Deutsches Museum in a Faraday cage with spark space.

The effect by which the electromagnetic field inside a conductor in equilibrium is zero, canceling out the effect of external fields, is known as Faraday cage. This is because, when the conductor is subjected to an external electromagnetic field, it becomes polarized, in this way it is positively charged in the direction in which the electromagnetic field goes, and negatively charged in the opposite direction. Since the conductor has been polarized, it generates an electric field equal in magnitude, but opposite in direction, to the electromagnetic field, so the sum of both fields inside the conductor will be equal to 0.

Entrance to a Faraday room.

It manifests itself in many everyday situations, for example, the malfunction of mobile phones inside elevators or buildings with a steel mesh structure. One way to check it is with a radio tuned to a Medium Wave station. By surrounding it with a newspaper, the sound is heard correctly. However, if you replace the newspaper with aluminum foil, the radio stops making sounds: aluminum is an electrical conductor and causes the Faraday cage effect.

This phenomenon, discovered by Michael Faraday, has an important application in airplanes or in the protection of delicate electronic equipment, such as hard drives or radio and television repeaters located on mountain tops and exposed to electromagnetic disturbances caused by storms.

History

In 1836, Michael Faraday observed that the excess charge in a charged conductor resided solely on its exterior and had no influence on anything enclosed within it. To demonstrate this fact, he built a room lined with metallic foil and allowed high-voltage discharges from an electrostatic generator to strike the outside of the room. He used an electroscope to show that there was no electrical charge present inside the room's walls.

Although this cage effect has been attributed to Faraday's ice tray experiments conducted in 1843, it was Benjamin Franklin in 1755 who observed the effect by lowering an uncharged ball of cork suspended from a silk thread through a opening in an electrically charged metal box. In his words, “the cork was not attracted to the inside of the box as it would have been on the outside, and although it touched the bottom, when it was removed it was not found electrified (charged) to the touch, as it would have been touching the outside. The fact is unique." Franklin had discovered the behavior of what is now referred to as a Faraday cage or shield (based on Faraday's later experiments, which duplicated the Franklin cork and box).

Operation

The operation of the Faraday cage is based on the properties of a conductor in electrostatic equilibrium. When the metallic box is placed in the presence of an external electric field, the positive charges remain in the lattice positions; the electrons, however, which are free in a metal, move in the opposite direction to the electric field and, although the total charge of the conductor is zero, one of the sides of the box (on which the electrons accumulate) stays with an excess of negative charge, while the other side runs out of electrons (positive charge).

Theoretical demonstration

Suppose the conductor has no electrostatic equilibrium. Assuming that the charge inside the conductor is zero, the potential V inside the conductor satisfies Laplace's equation, where R is the region occupied by the interior of the conductor:

► ► 2V=0Русский Русский r한 한 R{displaystyle nabla ^{2}V=0qquad forall mathbf {r} in}

Since the conductor is in equilibrium on its surface there are no currents, so the potential on its surface is constant:

V日本語S=V0{displaystyle VIND_{S}=V_{0}}

By virtue of the potential uniqueness theorem, the potential that satisfies such conditions is unique and it can be seen that the solution is trivially:

V=V0Русский Русский r한 한 R{displaystyle V=V_{0}qquad forall mathbf {r} in R}

The electric field inside will be given by the potential gradient:

E=− − ► ► V=0{displaystyle mathbf {E} =-nabla V=0}

So the electric field inside the conductor is zero. It is a consequence of Gauss's law, which says that inside a hollow conductor, the field is zero.