I am looking to find the magnetic flux of a cylindrical magnet as it passes through a coil. I am aware of the complexity of magnetism, however, i am only looking for a conservative approximation of the magnetic flux. I found the formula ΦB = B · A, but is my understanding that the magnetic field will not be constant over the loop. How do I account for this in the calculation? Also, is the equation asking for the cross-sectional area of the solenoid, or the area of the actual piece of wire used to make the coil?