In the maxwell-faraday equation, the voltage around a loop is proportional to the rate of change of the magnetic flux. If voltage is constant over time, does the magnetic flux continually increase to +/-infinity (for example, integrating both sides by delta time)?

Ampere's circuital law seems to suggest the magnetic field will be constant, but Maxwell-Faraday law seems to suggest otherwise in this situation.

Question

In the maxwell-faraday equation, the voltage around a loop is proportional to the rate of change of the magnetic flux. If voltage is constant over time, does the magnetic flux continually increase to +/-infinity (for example, integrating both sides by delta time)? 

Ampere's circuital law seems to suggest the magnetic field will be constant, but Maxwell-Faraday law seems to suggest otherwise in this situation.

irishboy123 · Answer

as $$\mathcal{E} = -{{d\Phi_B} \over dt}  = const$$ then $$\Phi_B = \alpha t + \beta$$

but not sure how this follows: "Ampere's circuital law seems to suggest the magnetic field will be constant"