Need Mathematical Help to Compute Magnetic Force

As you see the magnetic field is distorded and has a total different aspect as with a single magnet. The field is as in the picture when, as in your sketch, the poles have same polarity. In fact you can without too much error consider the superposition of the two fields considered as independent if you do not reach the saturation in the attracted part.

Hope it will help.

This is a situation where even a simple soft for magnetics is more usefull as any mathematical approach.

I thought it could help to have the fiel as well in the other relative position of the 2 PM.

Yo guest ,

Take a look here , they got a demo for simulations you want somewhere.

Comsol

I got one from them via their forum.

T L.

Excellent effort by everyone.I do understand that magnetic field lines do get distorted. I am looking for a mathematical formula. I got confused from Wikipedia. Let me explain my dilemma.

In physics we know when there are two forces operating at 90 Deg, the resultant force is computed by vector addition. Now we have two magnets with different B or flux density and different area of cross section. So which will dominate and push which magnetic force away and by what angle. I expect this to follow trapezoidal vector addition theory. Which parameter of magnetic component should i use here?

Could you please explain the "trapezoidal vector addition theory" I must recognize but I never heard about.

If you want to compute the force you can use the formula F= B²*A/(2*µo). The problem will be to define "B". This was the reason I gave you the possibility to see how fields are distorted in the 2 relative positions of the magnets.

Tahnk you for your effort.

Let us say there is a force Fx and Fy operating at a inclusive angle of Ө. Then the resultant vector is Fr. I have tried to put down my requirements. Wikipedia's formulas do not help to solve here. I need to specifically understand & predict which magnetic line will reach where

If your only knowledge in magnetics rely on wikipedia then you should not claim to be a specialist as you wrote in the other thread.

In fact you do not think "magnetics" since your knowledge is VERY limited. As for the other thread I can only recommend to learn more in order to master the problems.

When I say that you do not know enough about magnetics it is a statement not an insult and I wanted to explain how you should consider the solution. May be you read somewhere that the relative permeability of soft magnetic materials is very high with respect to the one of air which is 1. Due to this property the magnetic lines have at the surface of a soft material ≈ 90° angle with the surface.

The following pictures show the trajectories in the 2 above mentioned cases if with this input you still are not able to solve your problem then better take a book and learn more.

With the 2 PM with same direction toward the pole piece (square between PM ends)

The PM poles are contrary near to the pole piece. As you can notice the magnetic lines change the absolute angle but between pole piece surface and PM the angles are always same near to 90°. Approximation also due to the dimensions of the mesh which in both cases is pretty rough.

This shows how difficult it can be to answer "mathematically" to your question.

By the way what is the trapezoidal sum? you still did not answer what you represent is a parallelogram sum. Are both the same ?

Thank you MASTER. I am learning Magnetics. I have never claimed I am expert. I do appreciate your giving me some kind of simulation. Kindly let me know the link.

Let me specify my need. Say there is a PM B max = 0.4 T and another 0.2 T. Physical dimensions as shown in my drawing for magnet x and magnet Y can be different. Say both are in repelling situation - alternate 1 in your diagram. I would like to see flux lines of magnet x diverted more and of magnet y diverted lesser.

As far as trapezoidal diagram to find net result of two forces acting at an angle theta - I need not explain- you are aware I suppose. I was trying to find out whether I should use flux Ø or flux density B to try and compute the final result. Simulation involves assumption of software engineer, but I wish to understand myself through mathematics.

Thank you for you "fine" irony! I am by far not a "Master" but I worked several years in development of magnetic actuators. The computations (simulations) were made by me so that I have no link to give, you may try to find a free or share ware soft by using one of the search engines.

A few questions : how do you know that the field has 0.4 and 0.2 T? Field intensity depends on configuration of the space where the field is considered and of the "power" the PM have. The force depends as you saw on the area. What is the form of the piece interacting with the 2 fields? What kind of material is it from?

To give you a feeling of the mesh influence I made for the other case than the one you mention 2 more simulations with fine and very fine meshing the results are :

a mesh finer than the first used

a mesh even finer. As you see the force lines are perpendicular to the pole piece (soft iron) and you can thus use the equation I gave. You may notice a detail: the colour in the pole piece being different shows that the field intensity is not uniform i.e. the soft takes into consideration the magnetic property of the pole piece.

The problem is ONLY to know how big is B in the different sections. A second remark in the equation you find B^2 which means that ONLY the field density matters and not its direction. All ways if you interact with a passive component the force is trying to reduce the distance (gap).

Now, as I wrote, if with all I gave you still are not able to find the solution then take a book and learn more.

You have a problem with the meaning of words: trapeze is a quadrilater (polygon with 4 sides) with only 2 sides parallel, parallelogram is a 4 sides polygon and 2 by 2 parallel to each other. Your figure was right but the name you gave wrong.

Do not forget that engineering is a PRECISE profession and every word has a meaning if you do not use it right nobody understands what you want.

It is very often the case on this forum.

I was looking for this hint. It appears that F is proportional to B and not Ø (which is B*A). The puzzle is the formula has B^2 but only A in the numerator- hence I have not been comfortable- if there are two PM with B as flux density and area = A1 & A2, which will you take - smaller or bigger one?

According to my last statement I do not make any comment any more better take from the college library a book an magnetics and read it. I do not want to appear as the one to play the "master" role. In the book you will find why it is B^2 and all what you need to solve the problem.

Of course wikipedia and books say F= (B^2)*A/ 2υo. But this formula has many assumptions. It assumes magnets of same strength kep face to face etc. Anyway- I have picked up some hint. Thanks.