$\text{Flux through outer coil } \phi_{outer} = (\mu_0 nkt e^{-\alpha t})4\pi r^2$

$\text{Induced EMF } \xi = -\frac{d\phi}{dt} = -C e^{-\alpha t}(1 - \alpha t)$

$ \text{Induced Current } I = \frac{\xi}{R}$

At t = 0 $ I_{induced} \text{is negative}$