Answer the following:
(a) State Biot - Savart's law and express this law in the vector 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

### Step-by-Step Solution:

#### (a) State Biot-Savart's Law and its Vector Form

1. **Definition of Biot-Savart's Law:**
Biot-Savart's 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 \( I \), the length of the current element \( d\mathbf{l} \), and the sine of the angle \( \theta \) between the current element and the line connecting the element to the point where the magnetic field is being calculated. It is inversely proportional to the square of the distance \( r \) from the current element to the point.

Mathematically, this can be expressed as:
...