induced emf in a solenoid due to a rotating magnet

Aug 2019
Hey, I have come up with an idea for my EEI to measure the emf induced in a solenoid by a rotating magnet when the solenoid is not directly above the magnet (such that the magnetic field is not uniform). Previously I had to perform an experiment where the solenoid was on axis (see picture) and now I plan to further the experiment by moving it up and down (increasing height from the magnet) and left and right (increasing horizontal distance from the magnet) and I was wondering if anyone could point me in the right direction for deriving a formula for the off axis emf. Currently below are the two formulas for the on axis emf.

In the experiment it will be possible to measure the emf and thus the V and then calculate the field strength at that point (As N, w and A are constant). This field strength can then be used to determine the magnetic dipole moment, however it could also be used to check what factors affect the strength. So far I'm guessing the off axis magnet will only be affected by distance from the magnet, and thus only the z factor in the final formula will affect the field strength and this could be tested by measuring the dipole and using theoretical z values to find field strength, and comparing this to experimental values of field strength (However I cant check this until I perform the experiment this week).

But apart from that I could imagine the angle between the solenoid and the magnet having an effect, however I can't see how I would derive a theoretical formula for it at this point in time

emf = -wNBAsin(wt)
Where emf is induced in solenoid
w is angular frequency
N is number of turns in the solenoid
B is the magnetic field strength
A is the area of the solenoid

V = wNBA
V is the voltage in the solenoid
w, N, B, A as before

B = u/2pi * 2*U / z^3
B is field strength
u is constant 1.26*10^-6
z is the distance from the centre of the magnet along the axis
U is the magnetic dipole moment

Any help would be appreciated