# Coil output from variable magnetic field

If I put a coil with X Henry value and N turns in a variable magnetic field of Y Tesla peak value (coming from another coil excited by A sin(wt) signal), how to calculate the output voltage across the coil and the current running in this coil? I am designing a coil and a conditioning circuit to measure the value of the magnetic field. The output of the coil will be analyzed by the conditioning circuit in terms of magnitude and phase. I could know the field at a point by using ANSYS Maxwell software but I just used measurement point not real coils and the software gives me the B and H directly. Now from these values, I want to estimate the power level (coil output voltage or current) so I can design the system accordingly, for instance, the AWG of the coil wire and if I will need an amplifier or not, etc.

The open circuit output voltage is $$\N\frac{d\Phi}{dt}\$$ so, if you can position the coil so that it receives the largest amount of $$\\frac{d\Phi}{dt}\$$ you will get the largest peak-to-peak output voltage. Clearly, if the N turns have a cross sectional area that allows more flux ($$\\Phi\$$) to enter then you also get a larger output voltage. More cross section usually means more voltage. More N means more open circuit voltage.

A higher operating frequency can sometimes mean a higher $$\\frac{d\Phi}{dt}\$$ except in a regular transformer where the magnetization inductive reactance rises linearly with frequency and $$\\frac{d\Phi}{dt}\$$ remains constant for a given excitation voltage.

If the coil is loaded so that a significant current is drawn then things get more complex unless the coupling is close to 100% (as in a regular transformer). In non 100% coupled scenarios, you need to try and work out what the mutual inductances are so that you can estimate the output voltages when current is being drawn.

However, you can "know" k (the coupling factor) by studying the open circuit voltage and this can help you find the mutual inductances. It rapidly becomes a non-trivial exercise though.

• If this answer gives you what you need, you can mark it as "accepted". – Andy aka Apr 11 at 11:39