Calculating magnetic field as a function of magnet size

[eman3]

I want to determine how large a magnet I need in order to get a given field a certain distance away from the surface.

An N48 neodymium magnet has a Bremanence of ~1.47T. How does the physical size of the magnet affect the field a given distance away?

https://www.physicsforums.com/showthread.php?t=519563 seems to imply it's proportional to the volume. However, I'm unclear on how to apply the equations. I'm also surprised that no mention is given to the shape -- shouldn't a flat, thin magnet have its magnetic field fall off more slowly than a long, deep one?

 

[cmos]

That formula you refer to is for the field of a magnetic dipole and ONLY on the axis of the dipole. There, d is the distance from the dipole, it has nothing to do with the volume. In other words, the field of a static dipole decays as the reciprocal of the cube of the distance.

As an estimation to your problem, I am assuming that the (manufacturer?) specified field of 1.47 T is specified at the surface of the end of the magnet. Then, as long as you stay on the axis of the magnet, the field at a distance d away from the surface of the magnet is
B(d) = \frac{(\frac{H}{2})^3}{(d+(\frac{H}{2}))^3} \cdot 1.47 [\rm{T}] \; ,
where H is the height of the magnet.

 

[eman3]

Thanks! How did you derive that?

 

[cmos]

No problem; it's just the only way to enforce the d^-3 relation with the field referenced to the surface. Look up "magnetic dipole" for the derivation of the equation from the other thread.