Resumen de Magnetic Fields at the Center of Coils

Philippe Binder, Kaleonui Hui, Jesse Goldman

• In this note we synthesize and extend expressions for the magnetic field at the center of very short and very long current-carrying coils. Elementary physics textbooks present the following equation for the magnetic field inside a very long current-carrying coil (solenoid):

  B sol =μ 0 (NL )I, (1) where I is the current, N the number of windings, and L the coil length. It is obtained directly from Ampère's law, ignores end effects (hence it assumes an infinite coil), and is valid over the entire cross-section of the coil. The field is in the axial direction and it follows the right-hand rule convention. For N superposed loops of radius R each carrying current I, the multi-loop magnetic field at the center is given by B ml =μ 0 (N2R )I. (2)