A small coil of insulated wire wound around a nail in series with a 1.5 volt battery will create an electromagnetic field. Current flowing in any conductor creates a em field. A magnetic compass can be deflected if close enough.
A little more elaborate demonstration is a transformer. With alternating current or pulsating direct current a magnetic field is generated when current flows thru the windings. A current flow is generated in the secondary - an attached lightbulb can be the "detector" - a digital voltmeter is a bit more elaborate and has the advantage of broader range.