Moving coil Galvanometer:
It is a device used to detect small current flowing in the electric circuit.
Principle :
Moving coil Galvanometer is based on the fact that when a current carrying loop or coil is placed in the uniform magnetic field , it experiences a torque.
Construction:
it consists of a coil of copper wire wound on cylindrical soft iron core. The coil is pivoted in a uniform radial magnetic field provided by the concave shaped poles of a permanent magnet. The coil rotates freely about the pivot. A light pointer is attached to the coil. The pointer moves over a scale. A spring is attached to the coil to provide a restoring torque to the coil.
Theory :
Let B = Intensity of magnetic field
I = Current flowing through the coil
L = length of coil
b = Breadth of the coil
N = Number of turns in the coil
When current flows through the coil , it experiences a torque, which is given by :
$$\tau = NIABsin \theta$$
Where , $\theta$ is the angle made by the normal to the plane of the coil with the direction of the magnetic field. The plane of the coil is always parallel to the radial magnetic field , so $\theta = 90^{0}$
Hence , equ.(1) becomes
$$\tau = NIAB$$
This torque is known as the deflecting torque and is constant in any position of the coil in the radial magnetic field.
When the coil gets deflected , the spring is twisted and a restoring torque is developed in it.
If k is the restoring torque per unit twist (torsional constant) then the restoring torque for the deflection $\phi$ of the coil (pointer) is given by :
$$\tau^{'} = k \phi$$
Thus , the coil will stop rotating and come to rest ( equilibrium state ) , when
Deflecting torque = Restoring torque
$$NIAB = k \phi$$
$$I = \frac{k \phi}{NAB}$$
Where
$$G = \frac{k}{NAB}$$
G is called galvanometer constant
$$I= G \phi$$
$$I \propto \phi$$
Thus , deflection of the coil is directly proportional to the current flowing through it. Hence, we can use a linear scale in the galvanometer to detect the current in the circuit.
Use of a radial magnetic field in the moving coil Galvanometer :
A radial magnetic field produced by concave shaped poles of permanent magnet of galvanometer is always parallel to the plane of the coil. Torque produced in the coil of galvanometer is given by :
$$\tau = NIABsin \theta$$
For radial magnetic field , the angle between the normal to the plane of the loop and the magnetic field is 90°.
$$\tau = NIABsin 90^{0}$$
$$\tau = NIAB$$
$$\tau \propto I$$
Thus , when radial magnetic field is used , the deflection of the coil is proportional to the current flowing through it. Hence , a linear scale can be used to determine the deflection of the coil.
Figure of Merit :
It is defined as the amount of current producing one scale deflection in the galvanometer. That figure of Merit of galvanometer= $\frac{current}{deflection}$
The unit of figure of Merit is ampere / division