Can changes in a magnetic field travel easily over large distances? Here's what I did: I directed a laser onto a mirror that is hanging by a thread. The mirror is attached to the thread by two small magnets. The reflected beam of the laser is directed to a target. I then moved a hand held magnet in front of the mirror. The  magnets on the mirror responded by moving. Their movements were amplified by the laser, much the same way that a small movement of a rifle sight can mean large distances the farther the bullet travels. Also, the law of reflection doubles the movement too. So the result is a very sensitive device
Here's a close up of the mirror;
Here's the entire setup:
I posted a video for additional info.
The fields that I tested display great ranges. A small ceramic magnet has a field that reaches out to 100 feet. Small voltages produced measurable fields out several meters. The project left me with so many question, but I will narrow it to #1 below.


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*These results surprised me due to the fact that I was able to detect the fields interacting at distances in the 100 foot range for basic magnets, and close to three meters for a 1.5 volt battery sending current through a small loop of wire. Do these observations seem right? I can't come up with a more specific question other than are these the results one should expect? Are they reasonable?


Note: The video shows the observations.
 A: Fun experiment! I haven't run any numbers for whether the amplitude of oscillation you see seems plausibly caused by the magnetic fields generated by your handheld magnets, but I'll just answer your two questions.


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*Yes, magnetic fields are "tied to their source" in the sense that if the source moves, the magnetic field in its vicinity must also change. It's also true that if you introduce another source of magnetic fields, in this case the magnet you're moving with your hand, it will exert a force and a torque on the magnet you've hung from the string. See this Wikipedia page for more details.

*The fields do extend to infinity, in principle, though of course decreasing as the distance from the source increases. A rapid movement of the source would not cause the distant fields to "move" at speeds beyond $c$, however. I think that the concept of movement for a magnetic field is not so well defined, but I understand what you're saying. The answer is that changes in the field propagate at the speed of light. I'd recommend this book for more information.
As an aside, if you'd like to compare the angular displacement you observe with what you can expect from theory, you'll need to know the torsional spring constant of the wire with which you hung the mirror, and the total magnetic moment of each of your magnets. The motion of your handheld magnet exerts an oscillating torque on the hanging magnet, which acts as a driven harmonic oscillator. The amplitude you observe will depend on the torsional spring constant, the applied torque, the moment of inertia of your mirror+magnet assembly, and the damping. 
