Magnetic field at the centre of regular polygon of 'n' sides which is formed by wire, which carries current I and side of polygon is ‘a’ :-

The magnetic field at the center of a regular polygon due to a current-carrying wire can be calculated using Ampere's Circuital Law and the Biot-Savart Law. Here's how you can do it:

1. First, consider one side of the polygon. The magnetic field at the center due to this side can be given by Ampere's Circuital Law as B = μ0I/4πa, where μ0 is the permeability of free space, I is the current, and a is the length of the side.

2. The direction of the magnetic field due to this side can be given by the right-hand thumb rule. If you curl your fingers in the direction of the current, your thumb will point in the direction of the magnetic field.

3. Now, consider the entire polygon. Each side will contribute a magnetic field at the center. Since the polygon is regular, the angle between the magnetic field vectors due to adjacent sides will be 360°/n, where n is the number of sides.

4. The resultant magnetic field at the center can be calculated by vector addition of the magnetic fields due to all sides. This can be done by breaking each magnetic field vector into its components, adding the components, and then finding the resultant.

5. After doing the math, you will find that the magnitude of the magnetic field at the center is B = nμ0I/4πa sin(π/n).

6. The direction of the resultant magnetic field will be perpendicular to the plane of the polygon, following the right-hand thumb rule.

Please note that this is a simplified explanation and the actual calculation involves some trigonometry.