Electric field inside an ungrounded Faraday cage with current

[TVP45]

Current will indeed flow through the wall of a Faraday cage; they have lights in there.

A car is not a particularly good Faraday cage. It is made of a poor conductor and has large openings together with lots of "sneak" paths.

There are at least two documented cases of a person(the same person!) being struck by lightning while inside a car (well, actually a truck in one case).

 

[Shooting Star]

(From an earlier post of mine.) Member NoTime has mentioned the same thing.

In the ideal case, the Faraday cage should be an unbroken hollow conducting shell. Then there cannot be any electrical field inside due to outside fields. In practice, it is made of fine mesh, and connected to the ground, that is earthed.

A heavy duty properly grounded cage will prevent lightning from passing through. But, theoretically, it's possible to imagine an exceptionally powerful bolt of lightning entering it, because it's a mesh, not an unbroken hollow shell.