Magnetic Field of a Square Current Loop at an Arbitrary Point - Stefanou Antonios

This work offers a detailed analytical solution for the magnetic field produced by a square current loop, allowing for precise calculation at any arbitrary observation point (x, y, z) in space. The derivation is based on the Biot-Savart law, meticulously applied to each of the four linear segments constituting the square loop. Full expressions for the Cartesian components (B_x, B_y, B_z) of the magnetic field are presented, involving analytical integrals. To validate the general solution, the derived formulas are specifically applied to calculate the magnetic field at the loop's center, which successfully matches established textbook results. This paper serves as a valuable resource for students and researchers in electromagnetism requiring a complete and verified analytical framework for this common geometry.