Connect the coil to the Variac.  Turn the Variac up to about 40 and try to pick up some nails with the open end of the coil.  The further you turn up the Variac, the more nails you can pick up.

CAUTION:  The coil will heat up very quickly when run without the core.  Do this part of the demonstration for no more than 10 seconds at a time.

Now, insert the core and try the demonstration again.  You will find that you can pick up the whole pile of nails at a much lower setting on the Variac, showing the increase in magnetic power.

An interesting observation is to monitor the current of the coil when used as an electromagnet.  You will find that the current when used without the core can approach 70 amps when measured with a clamp meter.  However, the circuit breaker on the Variac is only rated for 15 amps, and the circuit breaker for the building outlet is rated at 20 amps......and yet we never blow either breaker when doing this demo.  The fact that the current is out of phase with the voltage by almost 90 degrees allows for this discrepant event.   If you do a calculation for the total power going into the coil you will find that the power factor is on the order of .01, which means the real current in the coil is much lower than the rated current on the circuit breakers.