Calculating the Magnetic Field due to a Bar Magnet

[anonymity]

I am trying to do a pre-lab assignment for an introductory calc-based E&M course, and it involves the calculation of a magnetic field due to a bar magnet.

My first inclination was to use the B = (mu/4pi) * (q (V x R ) / R³) equation, but I am quite certain that this is not the correct approach.

There is no single moving charge with velocity V which we can pinpoint, and Identifying every charge is clearly not the intent (integrating could be a possibility, but I am still convinced that there exists some other equation/idea that I can apply).

I don't have my book at hand, and we have not discussed anything like this in lecture yet (I do have my note-book).

Can someone point me in the right direction?

 

[BruceW]

In a bar magnet, there are no freely-moving charges. The magnetic field is created by bound currents. Close to the magnet, the field is difficult to model with an equation (since a bar magnet is only approximately dipole). But far from the bar magnet, the magnetic field is the same as for a perfect magnetic dipole. And the far-field strength does fall off with 1/r^3.
Search 'Dipole' on wikipedia, and go to the heading 'field of a static magnetic dipole' for more info ;)

 

[anonymity]

The question broke the magnet into two independent monopoles (one "positive"/North, one "negative"/south). It wants a specific, predictive equation.

It's good to hear that my suspicions were correct. What can I use to solve such a problem?

 

[BruceW]

On the webpage I said about, it gives the equation for the far-field strength of a dipole magnetic field. Since we want to model the bar magnet as two independant magnetic monopoles next to each other, the far-field is approximately the same as for a dipole. (So the equation will be correct, as long as you're not too close to the bar magnet).
But for the near-field, it depends on how you are going to model your magnetic monopoles. (Modelling a bar magnet as two magnetic monopoles isn't strictly correct, but it is useful to give an approximate idea of the true magnetic field).
I assume the question will want you to spread positive magnetic monopoles on the top side of the magnet, and negative monopoles on the opposite face.
I'm not exactly sure how magnetic monopoles work, but I assume they are the same as electric charges except that you use the constant $\mu$ instead of $\varepsilon$ and stationary magnetic monopoles affect the magnetic field in the same way as stationary electric charges affect the electric field.
Using this method to model a bar magnet is known as the Gilbert model, so search that to find more.

 

[anonymity]

Thanks for your responses. I talked to my professor today and think I've got it now.

Thanks again for your help.