Source: High school physics (Chinese)
Problem Sets:
Problem
For a given current through a galvanometer, the larger the pointer's deflection angle, the higher the sensitivity. Analyze qualitatively which factors influence the sensitivity of a moving-coil galvanometer.
The current sensitivity is $\dfrac{\varphi}{I} = \dfrac{NBA}{k}$. It increases with the number of turns $N$, the gap flux density $B$, and the coil area $A$, and decreases with the torsion constant $k$ of the spring.
At equilibrium the magnetic torque on the coil is balanced by the spring's restoring torque:
$$NBIA = k\varphi \quad\Longrightarrow\quad \frac{\varphi}{I} = \frac{NBA}{k}.$$The current sensitivity $\varphi/I$ is therefore proportional to $NBA$ and inversely proportional to $k$.
Hence the sensitivity is increased by:
(i) more turns $N$ on the coil;
(ii) a stronger magnetic field $B$ in the gap (e.g., a stronger permanent magnet and a smaller air gap, often with a soft-iron cylindrical core to make $\vec{B}$ radial and uniform in magnitude);
(iii) a larger coil area $A$ (longer and wider coil);
(iv) a smaller torsion constant $k$ of the spiral spring (a "softer" spring).