Question

Explain Biot-Savart law.

Hint:

The Biot-Savart law is crucial for calculating the magnetic field produced by a current-carrying conductor and plays a fundamental role in electromagnetism.

Answer 1

The Biot-Savart law describes the magnetic field \( \mathbf{B} \) generated by a small current element. It states that the magnetic field at a given point due to a current element is directly proportional to the current and the length of the current element, and inversely proportional to the square of the distance between the point and the current element. The mathematical expression is: \[ \mathbf{B} = \frac{\mu_0}{4\pi} \frac{I \, d\mathbf{l} \times \hat{r}}{r^2} \] where \( \mu_0 \) represents the permeability of free space, \( I \) is the current, \( d\mathbf{l} \) is the current element, \( \hat{r} \) is the unit vector from the current element to the observation point, and \( r \) is the distance between the current element and the observation point. \bigskip