Using Biot-Savart’s law, derive an expression for magnetic field at any point on axial line of a current carrying circular loop. Hence, find magnitude of magnetic field intensity at the centre of circular coil.

Explanation

To derive the expression for the magnetic field at any point on the axial line of a current-carrying circular loop using Biot-Savart's law, we will follow these steps:

### Step 1: Understand the Configuration
Consider a circular loop of radius \( A \) carrying a current \( I \). We want to find the magnetic field at a point \( P \) located at a distance \( x \) along the axis of the loop.

### Step 2: Apply Biot-Savart Law
The Biot-Savart law states that the magnetic field \( dB \) due to a small current element \( Idl \) at a distance \( r \) is given by:
\[
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