Question

State Biot-Savert law to infinitely long current carrying conductor.

Answer 1

The magnetic field \[d\vec B\]  at a point due to a small current element I \[d \vec l\] is directly proportional to the current II, the length element dl, and sin ⁡θ, and inversely proportional to the square of the distance r.

dB = \[\frac{\mu_0}{4\pi}\frac{I\,dl\sin\theta}{r^2}\]

In vector form,

\[d\vec B=\frac{\mu_0}{4\pi}\frac{I\,d\vec l\times \hat r}{r^2}\]

For an infinitely long straight current-carrying conductor, on integrating the Biot–Savart law, the magnetic field at a perpendicular distance rr from the conductor is

B = \[\frac{\mu_0 I}{2\pi r}\]

The direction of the magnetic field is given by the right-hand thumb rule.