Magnetic Fields due to Electric Current

Electric currents produce magnetic fields — that was Oersted's groundbreaking discovery in 1820. Before that, electricity and magnetism were considered separate phenomena. Now we know they are deeply connected, part of a single electromagnetic force. When current flows through a wire, a compass needle placed nearby deflects. This is the birth of electromagnetism. To quantify the magnetic field produced by current, we use the Biot-Savart law. It tells you the magnetic field contribution from a tiny segment of current-carrying wire. For a long straight wire, the field at distance r is B = μ₀I/(2πr). For a circular loop at its centre, B = μ₀I/(2R). For a solenoid (a coil of many turns), the field inside is B = μ₀nI, where n is the number of turns per unit length. The magnetic field is uniform inside a long solenoid. When a current-carrying wire is placed in a magnetic field, it experiences a force. This is the force that makes electric motors spin. The force on a straight wire in a uniform field is F = ILB sinθ. For a charged particle moving perpendicular to a magnetic field, it moves in a circle — the Lorentz force F = qvB provides the centripetal force. This is the principle behind cyclotrons, mass spectrometers, and the circular path of charged particles in the Earth's magnetic field (auroras). Ampere's circuital law provides another way to calculate magnetic fields from currents: ∮B·dl = μ₀I_enclosed. For symmetric situations (infinite wire, solenoid, toroid), it is easier than Biot-Savart. Understanding magnetic fields from currents is essential for electric motors, generators, transformers, MRI machines, and particle accelerators.