MP Board · Class 12 · Physics · Moving Charges and MagnetismExplain the principle, construction, working, and theory of a Moving Coil Galvanometer. Mention two advantages of a pivoted-coil galvanometer over a suspended-coil galvanometer.

Principle\nA moving coil galvanometer works on the principle that a current-carrying coil placed in a uniform magnetic field experiences a magnetic torque, which tends to rotate the coil, and the angle of deflection is directly proportional to the current flowing through the coil.

Construction\nThe main parts of a moving coil galvanometer are:

1. Magnetic Field System: A strong permanent horse-shoe magnet with cylindrical pole pieces provides a radial magnetic field.
2. Coil: A coil consisting of a large number of turns of insulated copper wire wound on a non-magnetic metallic frame (usually aluminum).
3. Soft Iron Core: A cylindrical soft iron core is placed symmetrically inside the coil to make the magnetic field radial and to increase the strength of the magnetic field.
4. Suspension System: The coil is suspended by a fine phosphor-bronze strip from a movable torsion head. A mirror attached to the suspension strip is used to measure deflection via lamp and scale arrangement.
5. Hair Spring: A hair spring (usually of quartz or phosphor-bronze) is attached to the lower end of the coil to provide a restoring torque and to act as a current terminal.

Working and Theory

• When an electric current $I$ flows through the coil of $N$ turns, each having area $A$, placed in a magnetic field of strength $B$, the magnetic torque $\tau$ acting on the coil is given by: $$\tau = NIAB \sin\alpha$$ where $\alpha$ is the angle between the normal to the coil and the magnetic field vector.
• Due to the cylindrical pole pieces and soft iron core, the magnetic field is radial everywhere ($\alpha = 90^\circ$ and $\sin 90^\circ = 1$). Therefore, the deflecting torque becomes constant and maximum: $$\tau_{deflecting} = NIAB$$
• This deflecting torque rotates the coil, which twists the suspension strip. The twisted strip produces an opposing restoring torque proportional to the angle of twist $\theta$: $$\tau_{restoring} = k\theta$$ where $k$ is the restoring torque per unit twist (torsional constant of the suspension strip).
• At equilibrium, the deflecting torque equals the restoring torque: $$NIAB = k\theta$$
• Therefore, the deflection $\theta$ is: $$\theta = \left(\frac{NAB}{k}\right) I$$
• Since $N, A, B,$ and $k$ are constants for a given galvanometer, we get: $$\theta \propto I$$ Thus, the deflection is directly proportional to the current, making a linear scale possible.

Advantages of Pivoted-Coil over Suspended-Coil Galvanometer

1. Portability: Pivoted galvanometers are compact, rugged, and can be easily carried from one place to another without damage, unlike delicate suspended ones.
2. Convenience: They do not require strict vertical leveling or rigid vibration-free tables for operation.