The principle of moving coil galvanometer is that when a conductor carrying current is placed in a magnetic field, it experience a force. The construction of a moving coil galvanometer is as shown in the figure.
A rectangular coil is suspended in between the poles of a powerful magnet by means a phosphor bronze wire. The magnet is bored out cylindrically so that the field is radial.
A soft iron core is placed inside the coil to induce large number of magnetic lines. A mirror M is fixed on the phosphor bronze wire. A spring is fixed at the bottom of the coil.
Let B be the strength of the magnetic field, n be the number of turns in the coil, A be the area of the coil and I be the current flowing through the coil.
The deflecting couple produced in the coil = BIAn.
Due to this deflecting couple, the coil rotates and this couple is opposed by the torsional couple produced in the phosphor bronze wire.
The restoring couple produced in the coil =Cθ
Where, C is couple per unit twist of the wire and θ is the angle of twist which can be measured by means of a lamp and scale arrangement.
At equilibrium,
BIAn = Cθ
i.e., I = (C/BAn) * θ
since, C,B,A and n are constants, the defelction in the coil is directional in the coil is directly proportional to the current through the coil.