Ampère's Law

Magnetic field circulation around current-carrying conductors

Ampère's Law is one of Maxwell's equations relating the circulation of the magnetic field around a closed loop to the current enclosed by that loop. For a long straight wire carrying current I, the magnetic field at distance r forms concentric circles with magnitude B = μ₀I/(2πr), where μ₀ = 4π×10⁻⁷ T·m/A. Using the right-hand rule: thumb along current direction, fingers curl in the direction of B. For a coaxial cable (inner current +I, outer current -I), the field outside is zero because the net enclosed current is zero. Inside a solenoid with n turns per unit length, B = μ₀nI (uniform and parallel to the axis), while outside it is approximately zero. Ampère's Law is most useful when the magnetic field has high symmetry (cylindrical for wires, rectangular for solenoids), allowing B to be pulled out of the integral.