I Magnetic field strength of a stack of magnets

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The discussion focuses on the application of a formula for the magnetic field strength of a single cylindrical neodymium magnet when multiple magnets are stacked together. It suggests that the formula can be adjusted by replacing the length L with nL, where n is the number of stacked magnets. There is a debate about the correctness of the original formula, particularly concerning the signs used in the equation. Ultimately, it is concluded that the magnetic field on the z-axis for the stacked magnets is equivalent to that of a single longer magnet. The participants express gratitude for the insights shared in the discussion.
xzy922104
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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.
 
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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
 
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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 $$ \displaystyle{\displaylines{B(z)=\frac{μ_0M}{2}(\frac{z}{\sqrt{z^{2}+R^{2}}}-\frac{z+L}{\sqrt{(z+L)^{2}+R^{2}}})}} $$
Please reference your formula.
 
hutchphd said:
That formula looks incorrect to me. In particular the minus signs (except between the two terms.Maybe $$ \displaystyle{\displaylines{B(z)=\frac{μ_0M}{2}(\frac{z}{\sqrt{z^{2}+R^{2}}}-\frac{z+L}{\sqrt{(z+L)^{2}+R^{2}}})}} $$
Please reference your formula.
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.
 
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Thank you all for your help!
 
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