The Electrical engine can be powered by a Solar Panel. I recommend using the second tier Solar Panel and a Batbox between them, as well as applying the more EU efficient upgrade circuit to the Electrical Engine. That will let you build up a little extra power during the day which can then help power the Engine further into the night.
You can further improve on this by using an eternal day mystcraft age with no weather. No night and no storms means you always get full power.
The upgrade you are after is the Iron Electron Tube. You will need to get a small circuit board and a soldering iron. Right click with the soldering iron to open its crafting interface. Insert the iron electron tube, then the small circuit board. The completed circuit board is then placed in the left slot of the electrical engine.
Do not use any of the other electron tubes, they actually decrease efficiency.
To figure out how many panels and how many electrical engines you need:
It's 6 eu/t to generate 2 mj/t from 1 electrical engine. Adding the upgrade, it becomes 5 eu/t to generate the same 2 mj/t. Quarry can use 10 mj/t, but 4 moves pretty well. So, 2 engines does a decent job. This would require 10 eu/t, so 1 advanced and 2 normal. To max it out, you need 5 electrical engines, so 25 eu/t. This would be 3 advanced and 1 normal.
As soon as possible, get and use redstone conduit. It's even better than connecting straight to whatever you are powering. Add in a redstone energy cell for even more awesomeness, including being able to set the actual output. Both the conduit and cell can store MJs. In fact, the redstone cell can store 500,000!
That should be plenty to really get your rolling