Question #43411

A moving coil galvanometer has a rectangular coil of $N = 100$ turns and area $A = 2 \times 10^{-4} \text{ m}^2$. It is placed in a radial magnetic field such that the plane of the coil is always parallel to the magnetic field lines. However, due to an asymmetric pole piece design, the magnitude of the magnetic field at the coil's position varies with its absolute angular deflection $\theta$ (in radians) as $B(\theta) = B_0 (1 + \beta \theta)$, where $B_0 = 0.5 \text{ T}$ and $\beta = 2 \text{ rad}^{-1}$. The suspension wire has a torsional constant $C = 10^{-4} \text{ N m rad}^{-1}$. Due to a mechanical fault, the pointer shows a zero error, resting at a deflection of $\theta_0 = +0.02 \text{ rad}$ when no current is passed. Find the steady angular deflection $\theta$ of the pointer when a steady current of $I = 1 \text{ mA}$ is passed through the coil.