Torque on a coil and the moving-coil galvanometer

A galvanometer detects very small currents and shows their direction. A coil of many turns on a light aluminium frame is pivoted on jewel bearings between the curved poles of a permanent magnet, around a soft-iron core. Because the poles are curved, the field is radial: at every angle the sides of the coil are at right angles to it, so the magnetic torque is BIAN whatever the position, and it is proportional to I. Two spiral springs oppose the turning (they also carry the current in and out). Their torque is proportional to the angle φ turned: τ(spring) = cφ, with c in N·m per degree. The coil stops where the torques are equal, BIAN = cφ, so φ = (BAN ÷ c) × I. The deflection is proportional to the current, the scale is evenly spaced, and the pointer moves the other way if the current is reversed. The sensitivity φ ÷ I = BAN ÷ c grows with more turns, a stronger magnet or a larger area, and with weaker springs.