What is the simplest design to replicate Oerstead's experiment at home?
What is the simplest design to replicate Oerstead's experiment at home?
  
  I want to demonstrate what Oerstead did several centuries ago. He demonstrated that there is magnetic field near a current carrying wire.


That can be done very simply and easily. All you need is any simple magnetic compass, a piece of wire and a battery. It is best to use a single alkaline or zinc-carbon C-cell or D-cell. They produce only 1.5 volts, thus not a very high current, and are not susceptible to rapid overheating when shorted.

Simply align the wire with the compass as shown below. Connect the ends of the wire to the battery. The compass will deflect as shown. If you pinch the wire to the battery with your fingers the heat at the connection points could be a little uncomfortable, but not harmful if you don't do it for long.




  What is the simplest design to create a DC power supply that can produce about 16.25 ampere or more?


I believe the illustrated method produced something close to 16 amps. It produced more than 10 amps in my shorted meter leads. However the battery may not last long enough. Oersted did more than demonstrate that there is a magnetic field near a current-carrying wire. He also demonstrated that the field has a circular shape. If you want a power supply to demonstrate that continuously, I would recommend finding a transformer from which you can remove the secondary winding and replace it with a winding with fewer turns of larger wire so the secondary produces only 2 or 3 volts. Connect it to a suitable rectifier. Connect wire or wire plus some resistance that will result in whatever current the transformer is rated for.