Magnetic field due to infinitely long straight conductor carrying current
In this post, we will apply the Biot-Savart law to derive an equation for the Magnetic field due to an infinitely long straight conductor carrying current.
Magnetic field due to an infinitely long straight conductor carrying current – derivation
XY is an infinitely long straight conductor carrying a current I (Figure below). P is a point at a distance a from the conductor. AB is a small element of length dl. θ is the angle between the current element I dl and the line joining the element dl and the point P.
According to Biot- Savart law, the magnetic field at the point P in a vacuum due to the current element Idl is
![Biot-Savart law equation](https://physicsteacher.in/wp-content/uploads/2022/06/image-8.png)
![Magnetic field due to an infinitely long straight conductor carrying current - derivation](https://physicsteacher.in/wp-content/uploads/2022/06/image-9.png)
![](https://physicsteacher.in/wp-content/uploads/2022/06/image-10.png)
Thus, we can derive an equation for the Magnetic field due to an infinitely long straight conductor carrying current.
formulas of the Magnetic field due to a long straight current-carrying conductor
For a finitely long conductor in a vacuum, at a point at a distance a from the conductor, the magnetic field B = [(μ0 I)/(4πa)](sin Φ1 + sin Φ2)
For an infinitely long conductor in a vacuum, at a point at a distance a from the conductor, the magnetic field B = (μ0 I)/(2πa)
If the infinitely long conductor is placed in a medium of permeability μ, then at a point at a distance a from the conductor, the magnetic field B = (μ I)/(2πa)