# Loss of Field After Turning off Magnet Current

Q:
Hi, I have a question on induced magnetism in a coil: How long does it take for a magnetic field to disappear after the current through the coil is turned off, i.e. drops to 0 Amps? Is there a way to calculate it or is it instantaneous? Thanks!
- Vitto O (age 23)
Connecticut
A:

The answer for how rapidly the field goes away will depend on how the current is turned off. Is there still a circuit element, with finite electrical resistance (R), left to connect the two ends of the coil? If so, in the simplest case, the current will decay exponentially with characteristic time L/R, where L is the inductance of the coil. If instead a switch is opened, leaving extremely large resistance, the current still won't fall to zero instantly. The reason is that there's an induced electromotive force (EMF) pushing the current to keep going, and that EMF is proportional to the rate of change of the field. So an instantaneous change would produce an infinite EMF. A very rapid change produces a large enough EMF to drive sparks across the open switch. There's also some capacitance between parts of the coil, so even without sparks the current won't change instantly but instead would oscillate for a bit while dying down. So the whole scenario of the current dropping to zero instantly can't happen.

Still, it's worth asking whether there's some lag between the changes in current and the changes in field. There is, since electromagnetic effects only propagate at the speed of light, about 3*108 meters/sec. That delay is pretty small for most purposes. The field one meter away will take about 3 nanoseconds to respond the the current changes.

Mike W.

(published on 04/08/2015)

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