Magnetic field strength of a stack of magnets

[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.

 

[anuttarasammyak]

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

 

[hutchphd]

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 $$ \displaystyle{\displaylines{B(z)=\frac{μ_0M}{2}(\frac{z}{\sqrt{z^{2}+R^{2}}}-\frac{z+L}{\sqrt{(z+L)^{2}+R^{2}}})}} $$
Please reference your formula.

 

[xzy922104]

That formula looks incorrect to me. In particular the minus signs (except between the two terms.Maybe $$ \displaystyle{\displaylines{B(z)=\frac{μ_0M}{2}(\frac{z}{\sqrt{z^{2}+R^{2}}}-\frac{z+L}{\sqrt{(z+L)^{2}+R^{2}}})}} $$
Please reference your formula.

I found the formula in this paper, under the section titled "Cylinder".

 

[hutchphd]

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

 

[xzy922104]

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?

 

[anuttarasammyak]

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.

 

[xzy922104]

Thank you all for your help!