Moving Coil Galvanometer and Current Sensitivity

Construction. A moving-coil galvanometer consists of a small rectangular (or circular) coil

of many turns of fine insulated wire, wound on a light metallic (usually aluminium) frame, suspended

or pivoted so it is free to rotate between the concave, curved pole faces of a strong permanent

magnet. A fixed soft-iron cylindrical core is placed inside the coil, and, together with the

specially shaped concave pole pieces, this arrangement is deliberately designed to produce a

radial magnetic field -- one in which the field lines run radially outward from the core at

every point around the coil's circumference, so that the plane of the coil is ALWAYS parallel to

the field, at every angle of rotation, rather than only at one particular instant. A hairspring or

suspension fibre (of known, small torsional (restoring) constant $k$) provides the restoring torque

and, in many designs, also carries the current into and out of the coil; a pointer attached to the

coil moves across a graduated scale to indicate the deflection.

Why a radial field matters. From the torque result of Section 4.12, $\tau = NIAB\sin\theta$

depends, in general, on the angle $\theta$ between the coil's normal and the field -- a coil placed

in an ORDINARY uniform field would feel a torque that changes (and even reverses sign) as it turns,

giving a scale that is nonlinear and inconvenient to read. Because the concave pole pieces and soft

iron core specifically maintain the coil's plane PARALLEL to the field at every angle it turns

through, $\theta=90^\circ$ is maintained throughout the coil's full range of motion, so $\sin\theta=1$

ALWAYS, and the deflecting torque simplifies to the constant-coefficient expression

$\tau_{\text{def}} = NIAB\,I$ -- proportional to $I$ alone, with no angle-dependent factor left to

complicate the response.

Working principle: torque balance. When a current $I$ flows through the coil, it experiences a

deflecting torque $\tau_{\text{def}} = NBAI$ (using the radial-field simplification above), which

rotates the coil, twisting the suspension. As the coil twists through an angle $\phi$, the suspension

develops a RESTORING torque $\tau_{\text{res}} = k\phi$, proportional to the twist angle, exactly as

for any torsion spring. The coil comes to rest, and the pointer settles at a fixed reading, at the

equilibrium angle where the two torques exactly balance:

Since $N$, $B$, $A$, and $k$ are all fixed, constant properties of a given instrument, the deflection

$\phi$ is directly PROPORTIONAL to the current $I$ -- giving a linear, evenly spaced scale, the most

practically convenient possible response for a measuring instrument.

Current sensitivity. The current sensitivity $S_i$ of a galvanometer is defined as the

deflection produced per unit current:

A galvanometer with a HIGH current sensitivity gives a large, easily readable deflection even for a

very small current -- a genuinely more sensitive instrument. From the formula, current sensitivity

can be increased in several distinct ways: by increasing the number of turns $N$ (more turns means

more total force, hence more torque, for the same current); by increasing the field strength $B$ …