If you're asking whether you have to connect the fixture ground to the house ground, you do. The idea is to connect any exposed portion of a metal fixture to ground, keeping anything you would be able to touch from having a hazardous potential on it. The way to do this is to connect the fixture ground (which is connected to the metal chassis) to the building ground (which comes from your electrical panel).
To wire up a light bulb in the well house, first, ensure that the power is turned off at the circuit breaker. Use a suitable light fixture and connect the black (live) wire from the power source to the fixture's black wire, and the white (neutral) wire to the fixture's white wire. Ground the fixture by connecting the green or bare copper wire to the ground screw. Finally, secure the fixture, install the bulb, and restore power to test the light.
If you mean 2 bare copper wires those are the ground wires. Tie them together and then connect the light fixture ground wire which will be green or bare copper to those ground wires.
Typical house wiring in the United States is: Green or bare copper = ground White = neutral (Center tap of the feed transformer) Black or red = hot.
Most likely your "purple" was once black, and is the negative; to verify, trace "purple" to ground, or touch the leads of an ohmmeter to purple and ground. You should get "0" ohms at the correct wire. This assumes a negative ground.
If you're asking whether you have to connect the fixture ground to the house ground, you do. The idea is to connect any exposed portion of a metal fixture to ground, keeping anything you would be able to touch from having a hazardous potential on it. The way to do this is to connect the fixture ground (which is connected to the metal chassis) to the building ground (which comes from your electrical panel).
To wire up a light bulb in the well house, first, ensure that the power is turned off at the circuit breaker. Use a suitable light fixture and connect the black (live) wire from the power source to the fixture's black wire, and the white (neutral) wire to the fixture's white wire. Ground the fixture by connecting the green or bare copper wire to the ground screw. Finally, secure the fixture, install the bulb, and restore power to test the light.
If your house wiring is encased in armoured (metal) sheathing back to the panel, then you can secure the green ground to the ground screw in the box. Make sure the armoured cable connector is tight on the box. This should ground the light back to the panel. If you are on "knob & tube" I would suggest thinking about re-wiring the house.
If you mean 2 bare copper wires those are the ground wires. Tie them together and then connect the light fixture ground wire which will be green or bare copper to those ground wires.
There should be two wires in the box, black and white and possibly a bare one depending on the age of the wiring in the house. The fixture has two screws on the base. One wire goes on each screw. If there are short wires on the fixture, black to black and white to white. If there is a bare ground wire in the house box, it attaches to the body of the fixture. If there is no ground screw on the fixture, do not worry about it.
To answer this question fully the type of appliance has to be stated and its voltage.
At that point, you should verify the home wiring; make certain that the black wire IS, in fact, the "hot" wire and that the white wire IS in fact the neutral. If the house is wired properly, connect the new fixture with "black to black and white to white." If you aren't certain that the house wiring was done properly, contact a local electrician to perform the work for you. Connecting a light fixture improperly can be dangerous to you and to anyone who subsequently changes a bulb or otherwise comes in contact with the fixture.
You don't say "turn off" or turn on". Light should be connected black to black and white to white and ground to ground. If you connect white to ground it will work, but you are then using the ground wire for an unintended purpose. Neutral is bonded to Ground at the panel. Current on ground wire could cause ground loops and may cause GFCI to trip if you have them in your house.
It seems like you are describing the Red, Black, White and Ground in your electric panel. There is 240 VAC between Black and Red and 120 VAC between Black and White and 120 VAC between Red and White. The electric panel has two busses that supply 120 VAC on alternating breakers in your panel. Essentially, the Red turns into "black" in the panel for all practical purposes. If you have a 240 VAC circuit it essentially takes up to two vertical positions in your electric panel.
The National Electrical Code allows this change only if you upgrade the whole circuit. BUT ..If you are using this outlet only when the light is on, connect the black wires together and the white wires together. Ground wires together to the box also. IF THIS IS WITHIN 6 FEET OF A WATER SOURCE, IN A BASEMENT, GARAGE, OR OUTSIDE IT HAS TO BE GFI PROTECTED!!!!
You will have to check to make sure. Normally, with 4 wires, the black and red are both power for 220. White for neutral and bare for ground. If you are only using one leg of it, you would use the black, white, bare ones and cap the red one. Someone may have used the 4 strand because they had it or 220 was planned but not done or both the red and black are hot. You should be able to tell in the panel. Do the red and black both connect to separate breakers or to one or is the red not connected?
If you don't know how to install light fixture, I don't recommend that you do it by yourself. The installation theory is actually very simple - all you need to do is attach fixture on the ceiling (or any other place) and then connect the electrical wires (usually there are two of them). After that it's good to put the light cover over the fixture to improve the appearance.