Expression for Magnetic Field at Centre of Hexagon
The magnetic field at the center of a hexagon loop carrying current can be calculated using the Biot-Savart law. The Biot-Savart law states that the magnetic field created by a current-carrying wire at a point is directly proportional to the current, the length of the wire, and the sine of the angle between the position vector and the direction of the current.

Loop Configuration
- The current is moving in a hexagon shaped loop of side length a.
- The loop consists of six straight segments of length a each.

Calculating Magnetic Field
- To find the magnetic field at the center of the hexagon, we need to consider the contribution from each of the six segments.
- Since the segments are all the same length and carry the same current, the magnetic fields they produce at the center will also be the same.

Resultant Magnetic Field
- The magnetic fields produced by the six segments will add up at the center of the hexagon due to their symmetry.
- The resultant magnetic field at the center of the hexagon can be found by summing the magnetic fields from each segment using vector addition.
Therefore, the expression for the magnetic field at the center of the hexagon loop of side length a carrying current can be calculated by considering the individual contributions from each segment and summing them up to find the resultant magnetic field.