Question #42734

Consider a Cartesian coordinate system where the $z$-axis is vertically upwards. A fixed, infinitely long straight wire lies along the $x$-axis and carries a constant current $I_1 = 5000 \text{ A}$ in the $+x$ direction. A straight conducting rod of mass $m = 10 \text{ g}$ and length $L = 1.0 \text{ m}$ is suspended by two massless, rigid, non-conducting rods of length $R = 0.2 \text{ m}$ from the $x$-axis. The rod is always parallel to the $x$-axis and is free to swing as a pendulum in the $yz$-plane. A uniform external magnetic field $\vec{B} = 1.0 \text{ T} \hat{k}$ is present in the region. The swinging rod is part of a closed electrical circuit containing a resistor, with the rest of the circuit arranged such that it does not experience any magnetic force or contribute to the motional EMF. The resistor has a color code: Brown, Black, Silver, Gold. At a certain instant, the pendulum passes through its lowest point (on the negative $z$-axis) with an angular velocity $\omega = 5 \text{ rad/s}$, moving in the $+y$ direction. Calculate the total tension $T$ in the two suspending rods at this instant. (Take $g = 10 \text{ m/s}^2$ and $\mu_0 = 4\pi \times 10^{-7} \text{ T}\cdot\text{m/A}$. Ignore the self-inductance of the circuit.)