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.

 

[sardar]

I can provide some insight into your question about calculating magnetic field as a function of magnet size. The magnetic field produced by a magnet is indeed proportional to its volume, as stated in the link you provided. This is because the strength of a magnet's field is determined by its magnetic dipole moment, which is directly proportional to the volume of the magnet.

However, the shape of the magnet does play a role in the magnetic field it produces. The magnetic field will be stronger at the poles of the magnet and will decrease as you move further away from the poles. This is why a flat, thin magnet may have a stronger field at a distance compared to a long, deep magnet. The shape of the magnet can also affect the direction and distribution of the magnetic field.

To calculate the exact magnetic field at a given distance from the surface of a magnet, you will need to use the equation for the magnetic field of a dipole, which takes into account the dipole moment, distance, and angle of the magnet. This equation can be found in most physics textbooks or online resources.

In order to determine the size of magnet you need to achieve a certain field strength at a given distance, you will need to rearrange the equation to solve for the volume of the magnet. Keep in mind that the strength of the magnet's field will also be affected by the material it is made of and any external factors such as nearby objects or other magnets.

I hope this helps to clarify the relationship between magnet size and magnetic field strength. It is important to consider both the volume and shape of the magnet when calculating the field at a given distance. Additionally, it is always best to consult reliable sources and perform your own calculations to ensure accuracy in your results.