Magnetic field strength of a stack of magnets

Click For Summary

Discussion Overview

The discussion revolves around the magnetic field strength of stacked cylindrical neodymium magnets, specifically whether a known formula for a single magnet can be adapted for multiple magnets stacked together. Participants explore the implications of stacking on the magnetic field and the validity of the formula used.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a formula for the magnetic field strength of a single cylindrical neodymium magnet and questions its applicability to stacked magnets.
  • Another participant suggests modifying the formula by replacing the length parameter L with nL, where n is the number of magnets stacked, indicating this seems reasonable.
  • Some participants express doubt about the correctness of the original formula, specifically regarding the use of minus signs, proposing an alternative formulation instead.
  • A later reply acknowledges that the original formula and the proposed alternative may be equivalent due to differences in reference points.
  • Questions are raised about whether stacking magnets affects the overall magnetic field and if the field can be treated as that of a single longer magnet.
  • One participant asserts that the magnetic field along the z-axis for the stack is the same as that of a single longer magnet.

Areas of Agreement / Disagreement

Participants express differing views on the correctness of the original formula and its adaptation for stacked magnets. There is no consensus on the best approach to modify the formula or the implications of stacking on the magnetic field.

Contextual Notes

Some participants reference specific papers for the formula, indicating potential differences in definitions or assumptions about the magnetic field's behavior in stacked configurations. The discussion includes unresolved questions about the mathematical steps involved in adapting the formula.

xzy922104
Messages
4
Reaction score
2
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.
 
Physics news on Phys.org
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:
  • Like
Likes   Reactions: 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 $$ \displaystyle{\displaylines{B(z)=\frac{μ_0M}{2}(\frac{z}{\sqrt{z^{2}+R^{2}}}-\frac{z+L}{\sqrt{(z+L)^{2}+R^{2}}})}} $$
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".
 

Attachments

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.
 
  • Like
Likes   Reactions: Klystron and berkeman
Thank you all for your help!
 
  • Like
Likes   Reactions: vanhees71 and berkeman

Similar threads

Undergrad Biot Savart law gives us magnetic field strength or magnetic flux density?
  • · Replies 1 ·
Replies
1
Views
2K
High School Magnetic fields attracting two disc-shaped magnets
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Relation between electric & magnetic fields in terms of field strength
  • · Replies 41 ·
2
Replies
41
Views
6K
Undergrad Calculating Magnetic field strength of a magnet
  • · Replies 198 ·
7
Replies
198
Views
16K
Undergrad Measuring Magnetic Field Strength of a Cylindrical Magnet
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad What's the field strength and pattern rules for bar magnets attached?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Temperature vs Magnetic Strength (Flux) relationship in ferromagnets
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Behaviour of Magnetic Fields Underwater
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Magnetic field inside a capacitor
  • · Replies 16 ·
Replies
16
Views
2K
High School Experiment issues (electromagnetism)
  • · Replies 42 ·
2
Replies
42
Views
3K