Galvanometer Deflection

α is deflection angle; k is torsional constant of the spring. At equilibrium, magnetic torque equals restoring torque. Deflection is proportional to current — galvanometer is a linear instrument.

Construction

A rectangular coil of $N$ turns and area $A$ is suspended in a radial magnetic field $B$ (maintained by cylindrical pole pieces + soft iron core). A phosphor-bronze spring provides restoring torque.

Working

Current $I$ through the coil → magnetic torque from mc19:

$$\tau_{\text{mag}} = NBIA$$

The radial field ensures $\sin\theta = 1$ for all deflection angles — torque is constant regardless of orientation.

At equilibrium, magnetic torque = spring restoring torque $k\alpha$:

$$NBIA = k\alpha$$ $$\boxed{\alpha = \frac{NBIA}{k}}$$

$\alpha$ is the deflection angle, $k$ is the torsional constant of the spring.

Linearity

Since $\alpha \propto I$, the galvanometer scale is linear — equal angular divisions correspond to equal current increments.

Current Sensitivity

$$S_I = \frac{\alpha}{I} = \frac{NBA}{k}$$

Increased by: larger $N$, stronger $B$, larger area $A$, weaker spring $k$.

Voltage Sensitivity

$$S_V = \frac{\alpha}{V} = \frac{S_I}{G} = \frac{NBA}{kG}$$

where $G$ is the galvanometer's own resistance.