Question #43033

A moving coil galvanometer has a coil of $N$ turns and area $A$, suspended by a wire of torsional constant $k$. Unlike a standard galvanometer, it is placed in a non-radial magnetic field. When the coil deflects by an angle $\theta$ from its zero-current equilibrium position, the angle between the magnetic field vector and the plane of the coil is exactly $\theta$. Additionally, the magnitude of the magnetic field at the coil's location varies with the deflection angle as $B(\theta) = B_0 \cos\theta$, where $B_0$ is a positive constant. A steady current $I$ flows through the coil, producing a steady deflection $\theta = \frac{\pi}{4} \text{ rad}$. If the uncertainty in measuring the deflection angle is $\Delta\theta$, what is the relative error $\frac{\Delta I}{I}$ in the determination of the current?