Induced EMF without motion?
What you've got is effectively a transformer, but with only one turn for your secondary winding.  Transformers don't work with DC input or output, because you can't induce a DC current with a fluctuating magnetic field. To induce a DC current, the magnetic field would have to increase in magnitude without bound, which would require the current through the primary (electromagnet) to increase without bound, which is obviously impossible.

The normal approach if you need DC output is to use a rectifier and filter capacitor. A single inline diode will function as a half-wave rectifier, but that discards half of your power. Four diodes forming a full-wave bridge rectifier overcomes that problem.