# Magnetic field strength of a stack of magnets

• I
• xzy922104
In summary, the formula for magnetic field strength between two magnets stackd together is the same as the formula for a single, longer magnet.

#### xzy922104

I know that for a single cylindrical neodymium magnet, the formula
$$\displaystyle{\displaylines{B(z)=\frac{μ_0M}{2}(\frac{z}{\sqrt{z^{2}+R^{2}}}-\frac{z-L}{\sqrt{(z-L)^{2}-R^{2}}})}}$$ shows the relationship between the magnetic field strength and the distance between the magnet. I was wondering if this formula still applies when several cylindrical magnets are stacked together, north pole to south pole? If it does not, is there any way that I could adjust it for situations involving stacked magnets? Thanks.

You assume that L in the formula of B(z) be replaced with nL where n is number of magnets stacked downward. It seems reasonable to me.
[EDIT]upward, not downward

Last edited:
xzy922104
xzy922104 said:
I know that for a single cylindrical neodymium magnet, the formula
$$\displaystyle{\displaylines{B(z)=\frac{μ_0M}{2}(\frac{z}{\sqrt{z^{2}+R^{2}}}-\frac{z-L}{\sqrt{(z-L)^{2}-R^{2}}})}}$$
That formula looks incorrect to me. In particular the minus signs (except between the two terms.Maybe $$\displaystyle{\displaylines{B(z)=\frac{μ_0M}{2}(\frac{z}{\sqrt{z^{2}+R^{2}}}-\frac{z+L}{\sqrt{(z+L)^{2}+R^{2}}})}}$$

hutchphd said:
That formula looks incorrect to me. In particular the minus signs (except between the two terms.Maybe $$\displaystyle{\displaylines{B(z)=\frac{μ_0M}{2}(\frac{z}{\sqrt{z^{2}+R^{2}}}-\frac{z+L}{\sqrt{(z+L)^{2}+R^{2}}})}}$$
I found the formula in this paper, under the section titled "Cylinder".

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xzy922104 said:
I found the formula in this paper, under the section titled "Cylinder"
Oh I see his origin is translated by L relative to what I was considering. They are the same then. .Good

anuttarasammyak said:
You assume that L in the formula of B(z) be replaced with nL where n is number of magnets stacked downward. It seems reasonable to me.
[EDIT]upward, not downward
Would stacking the magnets affect the overall magnetic field in some way? Would this magnetic field be different from viewing the stack as a single, longer magnet?

xzy922104 said:
Would this magnetic field be different from viewing the stack as a single, longer magnet?
As for the field on z axis , that you refer the formula, it is same as that of a single longer magnet.

Klystron and berkeman
Thank you all for your help!

vanhees71 and berkeman

## What is a magnetic field?

A magnetic field is an invisible force that surrounds a magnet and exerts a pulling or pushing force on other magnetic materials.

## How is magnetic field strength measured?

Magnetic field strength is measured in units called teslas (T). One tesla is equivalent to one newton of force per ampere of current per meter of distance.

## How does the strength of a magnetic field change with distance?

The strength of a magnetic field decreases as the distance from the magnet increases. The relationship between distance and magnetic field strength is described by the inverse square law, meaning that the strength decreases quadratically as the distance increases.

## What factors affect the magnetic field strength of a stack of magnets?

The magnetic field strength of a stack of magnets is affected by the strength of each individual magnet, the spacing between the magnets, and the orientation of the magnets. The amount of iron or other magnetic materials in the surrounding environment can also affect the field strength.

## How can the magnetic field strength of a stack of magnets be increased?

The magnetic field strength of a stack of magnets can be increased by using stronger magnets, decreasing the spacing between the magnets, and arranging the magnets in a way that maximizes the alignment of their magnetic fields. Additionally, surrounding the stack of magnets with iron or other magnetic materials can also increase the field strength.