Question #43416

A moving coil galvanometer has a coil resistance $R_g = 18\ \Omega$, $N = 100$ turns, area $A = 10^{-3}\ \text{m}^2$, and is placed in a radial magnetic field $B = 0.2\ \text{T}$. It is converted into an ammeter using a shunt resistance $R_s = 2\ \Omega$. The coil and pointer assembly has a total mass $m = 20\ \text{g}$ with its center of mass located at a distance $d = 1\ \text{cm}$ from the vertical pivot axis. The pivot has a torsional spring constant $k = 0.01\ \text{N}\cdot\text{m/rad}$. The entire ammeter is mounted on a horizontal centrifuge rotating at a constant angular velocity $\omega = 10\ \text{rad/s}$ about a vertical axis. The galvanometer's pivot axis is at a distance $L = 0.5\ \text{m}$ from the centrifuge axis. When no current flows, the torsional spring is relaxed and the pointer's center of mass is aligned exactly radially outward from the centrifuge axis. If a steady total current $I = 1.0\ \text{A}$ is passed through the ammeter, find the steady angular deflection $\theta$ of the pointer. (Assume $\theta$ is small so that $\sin\theta \approx \theta$).