Question

Write vector form of Biot–Savart law.

Hint:

For perpendicular wires, use Pythagoras theorem to find the resultant magnetic field when fields due to each wire are perpendicular components into the same direction (e.g., into the page).

Answer 1

The Biot–Savart law in vector form is expressed as: \[ \vec{B} = \frac{\mu_0}{4\pi} \int \frac{I \, d\vec{l} \times \hat{r}}{r^2} \] The variables are defined as: - \( \vec{B} \) represents the magnetic field. - \( \mu_0 \) denotes the permeability of free space. - \( I \) is the electric current. - \( d\vec{l} \) is an infinitesimal vector element of the wire carrying the current. - \( \hat{r} \) is the unit vector pointing from the current element to the point where the magnetic field is being calculated. - \( r \) is the scalar distance between the current element and the field point.