Question #42430

A small square loop of mass $m$, side length $a$, and electrical resistance $R$ is constrained to move along the positive $x$-axis on a smooth horizontal surface. A light inextensible string is attached to the loop, passes over a fixed massless pulley at $x = D$, then goes around a movable massless pulley, and is finally attached to a fixed peg at $x = D$. All string segments are parallel to the $x$-axis. A block of mass $M$ is attached to the movable pulley and slides on the same horizontal surface. A non-uniform magnetic field $\vec{B} = B_0 x^2 \hat{k}$ exists in the region. At $t=0$, the loop is at $x=0$ and is given an initial velocity $V_0$ in the $+x$ direction. Find the maximum $x$-coordinate reached by the loop before it momentarily comes to rest. (Assume $a \ll x$ and $D$ is sufficiently large)