Approximate inductance of a filamentary circular current loop

[LydiaAC]

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?

 

[cabraham]

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

 

[jlopezfis]

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