# 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

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 = [**(μ _{0} I)/(4πa)**]

**(sin Φ**

_{1}

**+**

**sin Φ**_{2}

**)**

For an infinitely long conductor in a **vacuum**, at a point at a distance **a** from the conductor, the magnetic field B = **(μ _{0} 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)**