(a) State Biot - Savart law and express this law in the vactor form.
(b) Two identical circular coils, P and Q each of radius R, carrying currents 1A and `sqrt(3)A`
respectively, are placed concentrically and perpendicular to each other lying in the XY
and YZ planes. Find the magnitude and direction of the net magnetic field at the centre
of the coils.

Explanation

### Solution:

**(a) Biot-Savart Law:**

The Biot-Savart Law states that the magnetic field \( \mathbf{B} \) produced at a point in space by a small segment of current-carrying wire is directly proportional to the current \( I \) flowing through the wire, the length of the wire segment \( d\mathbf{l} \), and the sine of the angle \( \theta \) between the wire segment and the line connecting the wire segment to the point where the magnetic field is being calculated. The law can be mathematically expressed as:

\[
d\mathbf{B} = \frac{\mu_0}{4\pi} \cdot \frac{I \, d\mathbf{l} \times \mathbf{r}}{r^3}
...