Magnetism - the proportionality constant question

AI Thread Summary
The discussion focuses on the derivation of the equation for the magnetic field (B) around a long wire, specifically addressing the origin of the 2π factor. The 2π arises from integrating around a circle of radius r, representing the circumference. Participants clarify that this magnetic field can be derived using Ampere's Law and the Biot-Savart Law. The equation mentioned includes the permeability of free space (μ0) and relates current (I) to the magnetic field at a distance (r). Understanding these principles is essential for grasping the behavior of magnetic fields generated by current-carrying wires.
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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!
 
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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).
 
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}
 
aha, thank you!
 
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