# 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.