Question #43034

A moving coil galvanometer consists of a coil of $N$ turns and area $A$, suspended such that it can rotate freely about the $z$-axis. It is placed in a permanent radial magnetic field of constant magnitude $B_0$. The torsional constant of the suspension is $C$. When no current flows, the coil is in equilibrium and its area vector points along the positive $x$-axis. When a steady current $I_0$ is passed through the coil, its area vector deflects by an angle $\theta_0 = 60^\circ$ towards the positive $y$-axis to reach a new equilibrium.

An infinite flat sheet carrying a uniform surface current density $\vec{K} = \frac{4 B_0}{\mu_0} \hat{k}$ is now placed in the $yz$-plane at $x = -d$ (where $d > 0$). The galvanometer is located at the origin. Assume the galvanometer components do not distort the magnetic field produced by the sheet.

A new steady current $I'$ is passed through the galvanometer, and it is observed that the coil deflects by the exact same angle $\theta_0 = 60^\circ$ towards the positive $y$-axis. Find the ratio $\frac{I'}{I_0}$.