Approximate inductance of a filamentary circular current loop

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SUMMARY

The inductance of a filamentary circular current loop can be approximated using the formula L = μ * π * radius / 2, where μ represents the permeability of free space. Numerical checks indicate that the average magnetic field across the loop is approximately 0.93 times the value at the center. Traditional methods often utilize a wire of finite radius, leading to divergence when the radius approaches zero. Understanding the physical significance of this approximation is crucial for accurate inductance calculations.

PREREQUISITES
  • Understanding of electromagnetic theory, specifically inductance.
  • Familiarity with the permeability of free space (μ0) and its value (0.4 * π μh/m).
  • Knowledge of logarithmic functions as applied in inductance formulas.
  • Basic principles of magnetic fields and their relationship with current.
NEXT STEPS
  • Research the derivation and applications of the formula L = μ0 * a * ln((8*a/b) - (7/4)).
  • Explore the concept of mutual inductance and its coefficients.
  • Study the effects of wire radius on inductance calculations in electromagnetic theory.
  • Investigate numerical methods for validating inductance approximations in circular loops.
USEFUL FOR

Students and professionals in electrical engineering, physicists studying electromagnetic fields, and anyone involved in inductance calculations for circular current loops.

LydiaAC
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Hello everyone,

I want to have a simple example of an inductance calculation.

The magnetic field normal to a filamentary circular current loop is not constant over the circle but if we approximate the value as that for the center, multiply by the area of the circle and divide by the current, we get

L=mu*Pi*radius/2

I checked numerically and it seems that the average magnetic field is in fact about 0.93 of the value at the center of the circle.

However, most books go straight to calculate the inductance using a wire of finite radius and the formula diverge when this radius is zero.

I am wondering how much physical significance have the simple calculation I described above. Any help?
 
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inductance of filamentary circular loop

L = μ0*a*ln((8*a/b)-(7/4)), where a = loop radius in meters, b = wire radius in meters, μ0 = free space permeability constant = 0.4*∏μh/m.

Does this help?

Claude
 
Check the coefficient of auto inductance and mutual inductance, this coefficients give a relationship between the magnetic flux and the current source
 

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