LEC 20 - Magnetic Moment of a Current Loop

This lecture begins by reviewing the Biot-Savart law and its application to find the magnetic field due to a long straight wire and a circular loop. It then derives the force between two parallel current-carrying wires, explaining that parallel currents attract and antiparallel currents repel, and notes that this was historically used to define the ampere. The main focus is on the magnetic dipole moment of a current loop, defined as M = I * A, where A is the area vector. The lecturer draws an analogy with electric dipoles, showing that the magnetic field far from a current loop along its axis is B = (μ0/4π) * (2M/r^3), similar to the electric field of an electric dipole. He then introduces a mathematical model replacing the current loop with two fictitious magnetic charges (monopoles) to simplify calculations, particularly for fields in the plane of the loop. This model yields the same results as the Biot-Savart law but with simpler mathematics. The lecture concludes by previewing the next topic: surface currents.