Define sensitivity of a moving coil magnesia galvanometer. Derive expression for current magnet. It is the sensitivity of a moving coil galvanometer.

Hint: The current sensitivity of a moving coil galvanometer is defined as the current in a micro ampere needed to consume a deflection of one millimeter at a scale 1m away from the mirror. A galvanometer’s sensitivity increases when the instrument displays greater deflection for a low current value.

Formula used:
$S = \dfrac{{NAB}}{k}$

Complete step by step answer:
Current sensitivity of a moving coil galvanometer is defined as the deflection produced in the galvanometer when a unit current flows through it.
If $d\theta $ is the change in the deflection produced by a small change in the current $dI$
So, sensitivity (S) of the galvanometer is given by
$S = \dfrac{{d\theta }}{{dI}}$
The current flowing through the moving coil galvanometer is given by
$I = \dfrac{k}{{nAB}}\theta $
where $\theta $ is the angle of deflection, n is the number of turns, A is the area, B is the magnetic induction and k is the couple per unit twist.
$ \Rightarrow \theta = \dfrac{{NAB}}{k}I$
$ \Rightarrow \dfrac{{d\theta }}{{dI}} = \dfrac{{NAB}}{k}$
Thus, sensitivity of the galvanometer is,
$S = \dfrac{{NAB}}{k}$
Hence, the current sensitivity of the galvanometer with a radial field depends directly upon N, A and B and is directly proportional to k.

Note:
Galvanometer is a device used to measure the magnitude of the small electric current. The current and its strength is determined by the movement of a magnetic needle, or that of a coil in a magnetic field. A moving coil galvanometer is a very sensitive device. The principle of the moving coil galvanometer is that when placed in an external magnetic field the current carrying coil experiences magnetic torque.