I am trying to simulate the magnetic flux density in 3D space. I can get B by following model which is a dipole's contribution to the magnetic field at a point.

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However, the strength of B is wrong when i test a point inside the magnet. Whats the strength of the field within a magnet? Is there any model to calculate the B-field inside a magnet?

  • $\begingroup$ Can't you match this formula for the exterior of the magnet with an uniform field inside ? This can be done for a sphere. If the magnet is long relative to its thickness, you may adjust two dipolar fields for the exterior part : \begin{align}\vec{B}_N &= \frac{\mu_0}{4 \pi} \Big( \frac{3(\vec{m} \cdot (\vec{r} - \vec{r}_N))}{|| \vec{r} - \vec{r}_N ||^5}(.-.) - \frac{\vec{m}}{||\vec{r} - \vec{r}_N||^3}\Big) \\ \vec{B}_S &= \frac{\mu_0}{4 \pi} \Big( \frac{3(\vec{m} \cdot (\vec{r} - \vec{r}_S))}{|| \vec{r} - \vec{r}_S ||^5}(.-.) - \frac{\vec{m}}{||\vec{r} - \vec{r}_S||^3}\Big)\end{align} $\endgroup$ – Cham Jul 18 '17 at 0:53

You cannot just simply use this equation to calculate the field inside the magnet because the integral is not convergent as written at $\textbf{r}=0$. Note that this is the real reason for distinguishing between the $H$ and $B$ fields. Either you control the shape of the volume surrounding the internal point at which you are calculating the field properly or use surface poles of proper distribution around the excluded volume of arbitrary shape to act as proxy for the shape of the excluded volume. All this is written very well in Chapter 2.3 of Fuller Brown: Magnetostatic Principles in Ferromagnetism.

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