Faraday cage from Gauss' law alone?

In summary, the properties of a Faraday cage can be derived from Gauss' law alone, although some may find the derivations unconvincing. Other derivations use a combination of Gauss' law and a closed line integral, which ultimately leads to the conclusion that the electric field inside the cage must vanish. However, there may be some cases that are not covered by these derivations, as discussed in an article from SIAM news.
  • #1
greypilgrim
548
38
Hi.

Is it possible to derive the properties of a Faraday cage from Gauss' law alone? I found some "derivations" which I find rather unconvincing since they somehow conclude from a vanishing flux that the E field must vanish as well.
Some slightly more elaborate derivations use a combination of Gauss' law and a closed line integral along a path partly inside the cavity and partly inside the conductor. Since all those integrals vanish, the E field inside the cavity must vanish as well, they conclude.

Does this really cover all possible cases?
 
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FAQ: Faraday cage from Gauss' law alone?

What is a Faraday cage?

A Faraday cage is a structure made of conductive material that is used to block electromagnetic fields. It works by redistributing the electric charges in the cage, cancelling out the electric field inside the cage and preventing any external electromagnetic fields from entering.

How does a Faraday cage work?

A Faraday cage works by utilizing Gauss' law, which states that the net electric flux through any closed surface is equal to the enclosed electric charge divided by the electric constant. The conductive material of the cage acts as a shield, redistributing the electric charges and cancelling out the electric field inside the cage.

What materials can be used to make a Faraday cage?

Any conductive material, such as metal mesh, aluminum foil, or copper, can be used to make a Faraday cage. It is important that the material is continuous and has no gaps or holes to effectively block electromagnetic fields.

What are the practical applications of a Faraday cage?

Faraday cages are commonly used in electronics to protect sensitive equipment from external electromagnetic interference. They are also used in buildings, such as hospitals and military facilities, to create shielded rooms for sensitive equipment and to prevent eavesdropping.

Can a Faraday cage protect against all types of electromagnetic fields?

A Faraday cage can protect against most types of electromagnetic fields, but it may not be effective against extremely low frequency fields or extremely high frequency fields. Additionally, if there are gaps or holes in the cage, it may not be completely effective in blocking all electromagnetic fields.

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