# Coil in magnetic field. Voltage step response

Say we have a coil in magnetic field as shown below (two empty squares are magnet poles). Now imagine we give some voltage pulse across the terminals.

I wonder how would current (its magnitude and rise/fall times) depend on angle between magnetic induction B and coil axis. What processes are involved? How is it possible to sense coil orientation using it? I also would like to see the equations.

The physical process

The voltage induced by a changing magnetic field is given by Faraday's law. Basically it says

voltage = turns of wire * (rate of change of magnetic flux)

Where magnetic flux basically means the total magnetic field passing through the coil.

If your coil is stationary, the rate of change of magnetic flux due to the magnet is zero. So, in the experiment your propose, the angle will have no effect. You won't be able to sense the magnetic field angle using the coil alone.

That said, you might be able to sense the presence of iron near the coil, because the inductance of the coil will be larger if iron is nearby (which will manifest as a slower rise and slower fall in the current).

• According to this paper (page 6) magnetic field somehow affects inductance too, but I can't understand how and why.infineon.com/dgdl/… Feb 9, 2017 at 12:13
• I'm pretty sure the physics explanation in that paper is incorrect. If it were correct, you would be able to build a lossless inductor that works differently in one current direction vs the other, and those don't exist. I expect the actual effect they're seeing has something to do with saturation of the magnetic material. You might want to look for other application notes that explain the effect.
– Luke
Feb 14, 2017 at 2:29
• I've thought about saturation too. The slope on magnetazation curve is more in direction of demagnatization. In induced field magnet's magnetization is affected. So induced field aligned with that of a permanent magnet will cause less dФ/dt than the one aligned in the opposite direction. If the induced field is turned off the magnet restores its initial magnetization due to some magnetic elasticity. What do you think about that hypothesis, Luke? Feb 14, 2017 at 5:26
• That explanation seems to fit to the paper: "The larger peak[less dФ/dt] will indicate the current that is in the same direction as the magnetic field caused by the permanent magnet". Feb 14, 2017 at 5:34
• Yeah, if I understood your explanation correctly, we're thinking the same thing. The permanent magnet starts to saturate when you try to magnetize it more in the same direction -> it adds less impedance -> the current peak from the same voltage pulse is higher. I think that's a reasonable explanation. Kind of reminds me of old magnetic technology like saturable reactors.
– Luke
Feb 14, 2017 at 6:54