If you magnetize an iron rectangle (or triangle, circle, disc with hole, . ) how do you calculate the magnetic fields inside the magnet? Do you use differential equations with boundary conditions? References are welcome.
B (uN / 2R) i i think is the magnitude of a magnetic field at the centre of a coil. But the strength in various different areas require advanced postgraduate mathematics and so called eliptical integrals! u permeability of free space N number of turns in coil R radius of a coil i current
The equations (magnetic part of Maxwell equations in static case and currents absent) are: div B 0 rot H 0 In addition you need magnetic properties of material in the form of relationship between H and B: BB(H). In linear case B μH, and solution is zero magnetic field everywhere. The trick is that in case of ferromagnetic materials the relationship between H and B is non linear hyperphysics.phy-astr.gsu.edu/hba. and non-zero solutions exist even in case of absence of external currents.
