I think you misread 'H' here. H in the question doesn't refer to the magnetic field strength and the formula you provided here refers to the H-field in a torus.
Also in your answer you disregarded the inductor. Bear in mind that once you open the circuit, you can't treat the inductor as a short-circuited wire. What you should do is to write out the KVL loop equation, bearing in mind the potential drop across the inductor is L(di/dt), where i is the time-varying current through the inductor. Then you'll get a differential equation which you then have to solve for the current. Plugging in a initial value will help you find the unknown constant of integration.