(a) State Biot - Savart law and ecpress it in the vector form.
(b) Using Biot - Savart law, law obtain the expression for the magnetic field due to a circular coil of radius r, carrying a current I at point on its axis distant x from the centre of the coil.

Explanation

### Solution:

**(a) State Biot-Savart Law and express it in vector form:**

The Biot-Savart Law describes how a current-carrying conductor produces a magnetic field in the surrounding space. It states that the magnetic field \( \mathbf{B} \) produced at a point in space due to a small segment of current-carrying wire is directly proportional to the current \( I \) flowing through the wire, the length of the segment \( d\mathbf{l} \), and the sine of the angle \( \theta \) between the segment and the line connecting the segment to the point in space. It is inversely proportional to the square of the distance \( r \) from the segment to the point.

Mathematically, the Biot-Savart Law can be expressed as:

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