hyphenator
Jul27-08, 04:41 PM
1. The problem statement, all variables and given/known data
How do I calculate the magnetic field of an irregularly shaped permanent magnet?
2. Relevant equations
Field of a magnetic point dipole:
\vec{B}(\vec{m},\vec{r}) = \frac{(\vec{m}.\vec{r})\vec{r}-\vec{m}\left\|\vec{r}\right\|^{2}}{\left\|\vec{r}\ right\|^{5}}
where
\vec{m} is the dipole moment (in Teslas, I think) and
\vec{r} = \vec{p} - \vec{b} is the vector that points from the base \vec{b} of the dipole to the point where the field is being evaluated
3. The attempt at a solution
I integrated this point dipole over a field of moments for a solid. The result was wrong because the integration treats the dipole field itself as a derivative.
The solid is a 1x1x1cm cube.
The moment field consists of unit vectors everywhere pointing along the Z-axis (only as a test, the field must be allowed to vary arbitrarily).
The surface field strength is supposed to be around 1.0 Tesla (within an epsilon), but the integration gave 5.7714e+10 Tesla, which tells me I did something very wrong indeed.
Note: I am using numerical integration without physical constants (because free space permeability is too small for machine precision), so I don't expect the results to be exact, just within a scalar multiple of the desired answer. I have adjusted the predicted results accordingly.
How can I use a field of moments for a solid to calculate the correct magnetic field?
I believe I need a "moment element" analogue of a volume element, but I have no idea how to make it.
How do I calculate the magnetic field of an irregularly shaped permanent magnet?
2. Relevant equations
Field of a magnetic point dipole:
\vec{B}(\vec{m},\vec{r}) = \frac{(\vec{m}.\vec{r})\vec{r}-\vec{m}\left\|\vec{r}\right\|^{2}}{\left\|\vec{r}\ right\|^{5}}
where
\vec{m} is the dipole moment (in Teslas, I think) and
\vec{r} = \vec{p} - \vec{b} is the vector that points from the base \vec{b} of the dipole to the point where the field is being evaluated
3. The attempt at a solution
I integrated this point dipole over a field of moments for a solid. The result was wrong because the integration treats the dipole field itself as a derivative.
The solid is a 1x1x1cm cube.
The moment field consists of unit vectors everywhere pointing along the Z-axis (only as a test, the field must be allowed to vary arbitrarily).
The surface field strength is supposed to be around 1.0 Tesla (within an epsilon), but the integration gave 5.7714e+10 Tesla, which tells me I did something very wrong indeed.
Note: I am using numerical integration without physical constants (because free space permeability is too small for machine precision), so I don't expect the results to be exact, just within a scalar multiple of the desired answer. I have adjusted the predicted results accordingly.
How can I use a field of moments for a solid to calculate the correct magnetic field?
I believe I need a "moment element" analogue of a volume element, but I have no idea how to make it.