The physics
A moving-coil meter is a coil on an axle between curved pole pieces. A spiral spring holds it back.
The curved poles make the field radial. So the coil's torque N B I A is the same at every angle.
The coil turns until the spring's torque k φ equals it. So the swing grows in step with the current.
N B I A = k φ φ / I = N B A / k φ / V = N B A / (k R)
A small shunt S side by side with the coil makes an ammeter. The coil keeps its own Ig.
Ig G = (I − Ig) S