Graphing magnetic field of two magnets in 3d space

[cashflow]

I never figured I would encounter a problem as hard as this. Basically, there are two magnets of varying strength at 2 different x, y, z coordinates. I need to come up with function(s) to graph the field in 3d space. Or, at least find the x,y,z point where the two fields cancel out (if they exist). I know I will need calc iii, but I have no idea where to begin with respect to this problem.

 

[Simon Bridge]

Have you been asked to come up with a general method or do you have a specific problem?

The starting point is your understanding of how magnetic fields interact.

The usual method is to exploit the symmetry of the problem to simplify it. For instance, if the two magnets are pointing right at each other the system has cylindrical symmetry so changing to cylindrical coordinates with the z axis through the magnets simplifies the problem immensely.

To find where the two fields cancel out - you need only write the equations for the field strength at each (x,y,z) point and find the minimum. Note: you also need the orientation and type of the magnets.

 

[cashflow]

We just need a general method. The two magnets can be at any location and any orientation (both known), and goal is to find out where the two fields cancel. Anyway, supposing the magnets are oriented towards one another, the problem becomes simple. However, what if one magnet has a 45 degree yaw and 12 degree pitch? The problem becomes confusing and I have no idea where to start... Any formulas I can use as a base to start? Thanks!

This is not for a school project.

 

[berkeman]

I never figured I would encounter a problem as hard as this. Basically, there are two magnets of varying strength at 2 different x, y, z coordinates. I need to come up with function(s) to graph the field in 3d space. Or, at least find the x,y,z point where the two fields cancel out (if they exist). I know I will need calc iii, but I have no idea where to begin with respect to this problem.

We just need a general method. The two magnets can be at any location and any orientation (both known), and goal is to find out where the two fields cancel. Anyway, supposing the magnets are oriented towards one another, the problem becomes simple. However, what if one magnet has a 45 degree yaw and 12 degree pitch? The problem becomes confusing and I have no idea where to start... Any formulas I can use as a base to start? Thanks!

This is not for a school project.

Have you considered getting simulation software like ANSYS?

http://www.ansys.com/Products/Simulation+Technology/Electromagnetics

For general solutions, you may need to simulate the geometries...

 

[Simon Bridge]

I was going to suggest using a pole model for the magnets, since the setup is not envisaged to be dynamic ...

You have two vectors for each magnet: position and orientation. You can find the field due to each magnet separately OK? You can write an expression for the total field or potential (whichever you like) at some (x,y,z)?

Of course - this is quickly non-trivial.
Which is why we use computers a lot.

Thing is, I don't know what it is that you find "confusing" about this - is it just that the expressions get very complicated?