Dimmers are notorious in terms of dirtying up AC. Do you have a hum with the dimmer switch completely off (or, conversely, all the way up)? If not, then it's the dimmer switch. If you still have a hum, troubleshoot as the posts above advise and try to isolate which component may be the source.
You can have an electric company in your area run a dedicated line from your wall outlet to your circuit breaker for fairly cheap. That way you amps will draw power meant for them and for them only.
