We need to apply Faraday's Law
in order to find the differential equation for the circuit. We choose a reference current to be in the clockwise direction. Then
The solution to this differential equation with the initial condition that is
The voltage across the inductor is not well-defined; because the electric field is nonconservative, the integral of depends on the path that you take. However, the problem clarifies this with the phrase ``as seen on an oscilloscope."