Class 12 > Unit # 18:Magnetic Fields > Galvanometer

Talha's Physics Academy

Electrical Instruments - Moving Coil Galvanometer

Describe the principle, construction and working of moving coil galvanometer. Prove that the angle of twist is directly proportional to the amount of current.

Moving Coil Galvanometer

"It is an electromechanical instrument used to detect or measure small electric currents in a circuit."

Figure: Structure of a moving coil galvanometer with horseshoe magnet, soft iron core, and suspended coil.

Principle

A galvanometer works on the principle that when a current-carrying coil is placed in a magnetic field, it experiences a magnetic torque that tends to rotate it. The deflecting torque is proportional to the current flowing through the coil.

Construction

A moving coil galvanometer consists of the following essential parts:

1. Magnetic Field: A horseshoe-shaped permanent magnet with concave pole pieces that produces a strong and uniform radial magnetic field.
2. Coil: A rectangular or circular coil made of multiple turns of insulated copper wire suspended in the magnetic field.
3. Metallic Strips (A & B): Two fine metallic strips used to suspend the coil and bring the electric current into and away from the coil. Strip 'A' acts as the primary suspension.
4. Soft Iron Cylinder (D): A stationary soft iron cylinder placed at the center of the coil to concentrate and radialize the magnetic field lines.
5. Spiral Spring (E): Attached to the bottom of the coil to provide a controlled restoring torque when the coil twists.
6. Mirror / Needle (M): A light pointer or small mirror attached to the suspension system for measuring the angular deflection of the coil.

Working

When an electric current flows through the suspended coil inside the magnetic field, a deflecting torque acts on the coil, causing it to deflect (twist) by a certain angle. As the coil twists, the suspension strip and spiral spring undergo elastic deformation, producing an opposing restoring torque. When the deflecting torque balances the restoring torque, the coil comes to rest at a deflection angle corresponding to the magnitude of the current.

Mathematical Derivation: Angle of Twist Proportional to Current

When current $I$ flows through a coil of area $A$ with $N$ turns placed in a magnetic field of induction $B$, the deflecting torque ($\tau_1$) is given by:

$\tau_1 = B I A N \cos\alpha \quad \text{--- (i)}$

Where:

• $B$ = Intensity of magnetic field
• $I$ = Current flowing through the coil
• $A$ = Area of the coil
• $N$ = Number of turns in the coil
• $\alpha$ = Angle between the magnetic field vector and the normal to the coil

Due to the radial magnetic field design using the soft iron cylinder, the magnetic field lines are always parallel to the plane of the coil ($\alpha = 0^\circ$), so $\cos(0^\circ) = 1$:

$\tau_1 = B I A N \times 1 = B I A N$

When the coil twists by an angle $\theta$, the spiral spring produces a restoring torque ($\tau_2$) that is directly proportional to the angle of twist $\theta$:

$\tau_2 \propto \theta \implies \tau_2 = c \theta \quad \text{--- (ii)}$

Where $c$ is the restoring torque per unit twist (torsional constant of the spring/suspension strip).

At equilibrium, the deflecting torque is balanced by the restoring torque:

$\text{Deflecting Torque} = \text{Restoring Torque}$

$\tau_1 = \tau_2$

$B I A N = c \theta$

Rearranging the equation to solve for the angle of deflection $\theta$:

$\theta = \left(\frac{B A N}{c}\right) I \implies \theta \propto I \quad \text{(Proved)}$

Conclusion:
Since $B$, $A$, $N$, and $c$ are constant for a given galvanometer, the angle of twist $\theta$ is directly proportional to the electric current $I$ passing through the coil ($\theta \propto I$). This linear relationship allows the galvanometer scale to be calibrated directly for precise current measurements.

© 2026 Talha's Physics Academy. All rights reserved.