Question #43414

A galvanometer coil has $N = 100$ turns, area $A = 10^{-2} \text{ m}^2$, and resistance $R_g = 8.0 \ \Omega$. An electric dipole of moment $p = 2.0 \times 10^{-3} \text{ C m}$ is rigidly attached to the coil such that the dipole moment vector is anti-parallel to the area vector of the coil. The system is placed in a region with a uniform magnetic field $B = 1.0 \text{ T}$ and a uniform electric field $E = 10^3 \text{ V/m}$, both pointing in the $+x$ direction.

Initially, the coil is held at rest with its area vector pointing in the $+x$ direction ($\theta = 0$). An ideal constant current source supplying $I_0 = 10.0 \text{ A}$ is connected across the galvanometer and a parallel shunt resistor $R_s$. The value of $R_s$ is chosen such that the coil is in neutral equilibrium at $\theta = 0$.

An instantaneous angular impulse $K$ is then applied to the coil. Due to electromagnetic damping, the coil rotates and comes to rest exactly at $\theta = \pi/2$. Assuming friction and self-inductance are negligible, what is the magnitude of the angular impulse $K$?