I A and ϕ inside a Faraday cage?

[cuallito]

Are A and ϕ always zero inside a Faraday cage, like E and B are?

If not, can its design be modified to accomplish that? If not, is there an analogous mechanism that'd always have A=0 and ϕ=0 inside?

 

[Orodruin]

No. Same answer as your other thread. The potentials are only physical up to gauge transformations. It therefore makes little sense to talk about the value of the potentials (unless you fully specify the gauge fixing).

 

[vanhees71]

If the em. field is zero somewhere, i.e., $\vec{E}=\vec{B}=0$, then $\Phi=\partial_t \chi/c$ and $vec{A}=-\vec{\nabla} \chi$ for an arbitrary scalar field $\chi$. The gauge potentials are not uniquely defined by the equations of motion describing a physical situation. That's, because Maxwell's electrodynamics is a gauge theory. The potentials do not have a specific physical meaning but the observable electromagnetic field $\vec{E}=-\partial_t \vec{A}/c - \vec{\nabla} \chi$, $\vec{B}=\vec{\nabla} \times \vec{A}$, which is a gauge-invariant quantity, has.