Question #43312

A stationary circular conducting loop of radius $r$, mass $m$, and specific heat capacity $s$ is placed in a uniform magnetic field directed perpendicular to the plane of the loop. The magnetic field varies with time $t$ as $B(t) = \beta t$, where $\beta$ is a positive constant. The initial resistance of the loop at $t=0$ is $R_0$. The resistance varies with temperature $T$ as $R(T) = R_0[1 + \alpha(T - T_0)]$, where $T_0$ is the initial temperature and $\alpha$ is the temperature coefficient of resistance. Assuming no heat is lost to the surroundings, negligible thermal expansion of the loop's dimensions, and negligible self-inductance, what is the time $t_0$ required for the resistance of the loop to become $2R_0$?