Can electromagnetic fields be measured from a distance? I know that direct measurements of electromagnetic fields can only tell information about the field near the probes, but I am curious if there is a way to measure the electromagnetic field in a not too distant point of space(about 1-2 meters).
 A: Unfortunately, NO, there is not a way to measure an electromagnetic field (in a vacuum) at a point without placing a probe at that point.  In a strongly nonlinear medium the refractive index and the local birefringence of the medium may be affected by the electromagnetic field in such a way that the field can be mapped out by distant sensors; but even in that case it would be necessary to use a laser or somesuch light source to probe the effects of the electromagnetic field on the medium.  And the medium itself could be considered to be a probe.
It's a bit ironic: we write field equations that assume we know the field everywhere, but there really isn't a way to measure the field everywhere.  Instead, we measure at a few points and use our knowledge of the apparatus and Maxwell's equations to infer the field values everywhere else.
A: Yes, they can. Suspend a first surface mirror from a thread. Attach the mirror to the thread with two small magnets. Direct a laser onto the mirror so that the reflected laser is projected on a distance target. Shake a magnet in front of the hanging mirror. The laser will show the mirrors reaction. A typical ceramic magnet should be detectable out to 100 feet. To detect a pulsating current through a wire create a wire loop, and with a hand switch pulse current through the wire.  See my video. It shows how it all works. https://youtu.be/53RVKc5R2bs
