I came across a formula F=[[sq(n*i)]*4*pi*10^(-7)*A]/2*sq(g). But the terms A and g aren't properly explained and also, the magnetic field of NdFeB core is completely neglected here.
You can determine pull force based on numerical fields solutions employ the methot of weighted Maxwell stress tensor and the classical vrtual work.
Formulas are great--but one must know how to apply them. For magnetic pull force calculations, the important parts are the magnetic field, the low-reluctance-area, A, through which the field passes at the gap, g, spanning low-reluctance paths. The force is F=A *B^2/2*mu_knot. For a traditional solenoid, a common expression for magnetic field is: B=Bsol=mu_knot*N*I/g, where g = gap. Then, F=mu_knot*A*(NI/g)^2/2 [same as your equation, without NdFeB.] For your situation with permanent magnet core, you must determine the total field, B=Btot = Bsol + BPM. Then use the first force equation above. Good luck.
Thank you. Your answer helped me a lot. If NdFeB is not a core, but a plunger in the air core solenoid, will the pull force vary? As i studied, it's different for different positions of permanent magnet from the centre of solenoid..?
Yes, the force can be quite sensitive to geometry, both of the stroke and the rest of the magnetic path. Also must beware of magnetic saturation, especially at corners in flux path. You must look carefully at the entire magnetic circuit.
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