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 vector form of Biot–Savart law is: \[ \vec{B} = \frac{\mu_0}{4\pi} \int \frac{I \, d\vec{l} \times \hat{r}}{r^2} \] where: - \( \vec{B} \) is the magnetic field, - \( \mu_0 \) is the permeability of free space, - \( I \) is the current, - \( d\vec{l} \) is a vector element of the current-carrying wire, - \( \hat{r} \) is the unit vector from the element to the field point, - \( r \) is the distance between them.