Time course of magnetic field formation (spatial distribution of field)

[Gotrobotfrien]

Hi All,

I've done a quick google, and I can't find anything obvious (first 3 pages) about the formation of magnetic fields, specifically, how does the distribution of magnetic field through space take place as an electrical coil is switched on?

As a secondary question, is it possible to "pinch" a region of space with temporally short, but spatially much more concentrated magnetic field? As in, say a steady state magnetic field generated by a coil is about 1T in the bore, how does it approach this value when switched on? Is there any oscillation (overshoot) in field strength before settling?

Thanks for any insights.

 

[chrisbaird]

When you switch on current through a coil, even if it is a DC current, you are going from 0 current to a non-zero current. This is a changing current. Changing currents radiate electromagnetic waves. The wavefront travels out away from the coil at the speed of light. You should be googling terms like "electromagnetic radiation". Many older cell phone antennas are simply little coils of wire with the current being turned on and off so that your voice data is carried away encoded in the radiated waves.

If you are asking how long it takes after switching on the DC current to have a static magnetic field, strictly speaking the answer is: forever. It will take an infinite amount of time for the wavefront to propagate out to the infinite ends of the universe and form a complete static field. What if we care only about points in some local region (say within some radius R) near the coil, and ask how long it takes for the field to become static in this region, the answer is still forever. The fields asymptotically approach a static configuration but technically never reach it. For practical purposes, you could describe the time it takes for the fields to become static as the time it takes to becomes constant to the 5th decimal place (or 6th, or 7th).