There is an existing question Why can an electric field escape from a black hole? which has a complex answer, not accessible to the layman.
The point of this new question is that the electromagnetic field is mediated by photons. Yet photons emitted at the surface of a black hole (of a large enough mass) will not be able to escape beyond the event horizon.
Would a large black hole have no measurable electric field beyond its event horizon, even if it carried a high charge at its surface?
