Need help understanding off axis electromagnet field strength equation

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SUMMARY

The discussion centers on the misunderstanding of the off-axis magnetic field strength equation for electromagnets, specifically the polynomial approximations provided on the referenced webpage. The user attempted to apply these equations beyond their intended range, resulting in unrealistic values for field strength, such as 1 Tesla at 5 cm from the solenoid, while the known center strength (B_0) is only 0.03 Tesla. The key takeaway is that polynomial equations for magnetic fields are valid primarily within the solenoid and should not be extrapolated outside this region. The user seeks a valid equation for calculating magnetic field strength outside the central core of the solenoid.

PREREQUISITES
  • Understanding of electromagnetism principles
  • Familiarity with polynomial equations and their applications
  • Knowledge of magnetic field strength measurements
  • Experience with solenoid configurations and their characteristics
NEXT STEPS
  • Research the Biot-Savart Law for calculating magnetic fields outside solenoids
  • Study the mathematical modeling of magnetic fields in three-dimensional space
  • Explore finite element analysis (FEA) tools for simulating electromagnetic fields
  • Learn about the limitations of polynomial approximations in physics
USEFUL FOR

Electromagnetic engineers, physics students, and researchers involved in designing and analyzing electromagnets and their field distributions.

Jake110
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I have this equation for the magnetic field strength of an electromagnet but it’s in the form of multiple polynomials. Here is the page where they all are:

http://www.netdenizen.com/emagnet/offaxis/solenoidoffaxis.htm

since it gives values for e_8 and p_8 I tried using the main equation up to the 8th power but when I plotted the parallel distance against the field strength I found that it increases drastically to the point where at 5cm away the field strength is 1 Tesla (the strength I already know is B_0 which is the strength at the centre of the electromagnet and that’s only 0.03 Tesla)

So obviously the way I tried using it is wrong because the field strength should decrease the further away your measuring.

Can anyone help me figure out how to use this equation?
 
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Read the page you linked carefully. Note that the polynomial represents approximately field strengths INSIDE the solenoid. As you have discovered, if you extrapolate polynomial approximations outside of the region it represents the values obtained become meaningless very fast,
 
damit, you wouldn't happen to know an equation for the field strength outside the central core would you?
 

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