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
Magnetic field due to an infinitely long straight conductor carrying current - derivation

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 = [0 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 = 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)

Magnetic field due to infinitely long straight conductor carrying current
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