Equation for magnetic moment, E-field and B-field

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SUMMARY

The discussion centers on the relationship between magnetic moments and electromagnetic fields, specifically addressing the absence of an electric field (E-field) when a magnetic moment is present. Patrick provides the formula for the magnetic field (B-field) generated by a magnetic moment (m), expressed as B = [3(m·r)r/r^5 - m/r^3], where r represents the position vector. The conversation confirms that while a magnetic moment generates a magnetic field, it does not produce an electric field.

PREREQUISITES
  • Understanding of vector calculus, particularly dot products.
  • Familiarity with electromagnetic theory, specifically magnetic moments.
  • Knowledge of magnetic field equations and their derivations.
  • Basic concepts of charge and current in closed loops.
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  • Study the derivation of the magnetic field from a magnetic moment using vector calculus.
  • Explore the implications of magnetic moments in classical electromagnetism.
  • Learn about the conditions under which electric fields are generated in electromagnetic systems.
  • Investigate the role of delta functions in electromagnetic field equations.
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Physicists, electrical engineers, and students studying electromagnetism who seek to deepen their understanding of the relationship between magnetic moments and electromagnetic fields.

pangsiukwong
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Hi!

When a charge/current moves in a closed loop, a magnetic moment is generated.
Is there any formula for connecting the magnetic moment to E-field and B-field?

Patrick
 
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A magnetic moment m (a vector) produces a magnetic field given by
B=[3(m.r)r/r^5-m/r^3] plus a delta function if r-->0.
The r in the numerators are vectors and . means the dot product.
There is no E field produced.
 

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