Approximate inductance of a filamentary circular current loop

In summary, the conversation discusses calculating the inductance of a filamentary circular current loop and the differences between using a finite radius wire and approximating the value at the center of the circle. The formula for inductance is provided and the significance of this simple calculation is questioned. Further information is also mentioned about coefficients of auto inductance and mutual inductance.
  • #1
LydiaAC
Gold Member
39
2
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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  • #2
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
 
  • #3
Check the coefficient of auto inductance and mutual inductance, this coefficients give a relationship between the magnetic flux and the current source
 

1. What is the formula for calculating the approximate inductance of a filamentary circular current loop?

The formula for calculating the approximate inductance of a filamentary circular current loop is L = (μ0 * N^2 * A) / l, where L is the inductance, μ0 is the permeability of free space, N is the number of turns in the loop, A is the area of the loop, and l is the length of the loop.

2. How does the number of turns in the loop affect the inductance?

The inductance is directly proportional to the square of the number of turns in the loop. This means that as the number of turns increases, the inductance also increases.

3. What is the significance of the area of the loop in calculating the inductance?

The area of the loop is a measure of the amount of current flowing through it. A larger area means a larger amount of current, and therefore a larger inductance.

4. Can the length of the loop affect the inductance?

Yes, the length of the loop also affects the inductance. A longer loop will have a larger inductance compared to a shorter loop with the same number of turns and area.

5. What is the unit of measurement for inductance?

The unit of measurement for inductance is the Henry (H). It is named after the scientist Joseph Henry and is equivalent to 1 volt-second per ampere (V·s/A).

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