I am trying to control an electromagnet with a signal from a small microcontroller (a BeagleBone Black). Obviously, I need to amplify the signal. I have a lead from a power source that I want to pass through to something when the pin on my board goes High (3.3v). I think that a relay is what I want here (correct me if I'm wrong), but have no idea how to find one that will do what I need. The separate power supply will range anywhere from 5 Volts 0.5 Amps to possibly 20 Volts 3 Amps. Because of the circumstances where I'll be using these relays, I would rather use solid-state relays so that there aren't more magnets than there needs to be in the vicinity.
Are relays what I'm looking for? If so, are relays that fit these specs available, and what exactly am I looking for?
EDIT: To add some more detail, it will be High for approximately 50-100 ms. For most of the time, the separate supply will be at 20 Volts 3 Amps, but I will be testing my stuff with it, so I may try it at higher or lower values.