Magnetism - the proportionality constant question

[dragon513]

Hi! Can anyone please tell me where this equation was derived from?
This equation is used to get the magnetic field (B).
I is current and r is the distance. And I think I understand the Meu. And yet I have no idea where the 2pi came from. I looked in my textbook, internet and asked friends but nobody seems to know.

Thank you!

 

[Tide]

That is the magnitude of the magnetic field carried by a long wire. I think you meant r instead of y in the equation you displayed. You obtain it by simple application of Ampere's Law and the $2\pi r$ comes from integrating around a circle of radius r (i.e. it's the circumference of the circle).

 

[dicerandom]

Well, that's the magnetic field from an infinite straight wire, which you can get using Biot-Savart:

$$d\vec{B} = \frac{\mu_0}{4\pi} \frac{I \vec{dl} \times \hat{r}}{r^2}$$

Biot-Savart is derived from Ampere's Law:

$$\int_C \vec{B} \cdot \vec{dl} = \mu_0 \int_S \vec{J} \cdot \vec{da}$$

 

[dragon513]

aha, thank you!