MAP OF THE FACTORY:
Map legend: 1 - entrance to the factory; 2 - passageways leading to the room with a Tesla coil; 3 - Tesla coil; 4 - computer terminal; 5 - exit to Old Olney
Use the stairs to get to the upper floor. You can finish this part of the quest in less than a minute, assuming you have a very high Science skill. If you do - hack into a very well protected computer terminal located to your right [#31] and unlock a nearby door. If you can't use the terminal, you'll have to go through the entire factory. It's going to be a long journey, but you'll also have a chance to earn a lot of experience points. Keep reading if you want to find out how to get to the room with the coil.
The entire warehouse is being patrolled by powerful sentry bots [#32], but thankfully you won't have to engage most of them in direct combat. Each time you'll get to an area with new sentry bots focus your efforts on finding a computer terminal. Hacking into the system will enable you to shut down the machines. Notice that you can destroy unactive bots and this will result in your main character earning valuable experience points without taking any risks. The same goes with every successful hacking attempt.
Proceed to the southern section of the factory, using stairs and balconies along the way. Once you found your way to a new balcony go to your right. Sadly you'll have to destroy one of the sentry bots in direct confrontation, so it would be a good idea to wait for Fawkes to join you. Once the machine has been destroyed use a computer terminal on the right wall [#33]. Hacking into the system not only will allow you to power down other bots, but you'll also disable radiation traps (first option from the list). This is a very important issue, because otherwise you would have to deal with large doses of radiation in the next corridor (20-40 rads per second!!).
Head forward. Once you're inside a new room use a computer terminal located on the left wall. You won't have to perform any particular tasks here, because all you want to do is to earn experience points for hacking into the system. Start moving west and unlock a new passageway [#34] using yet another computer terminal. You'll find a switch inside this dark corridor, as well as two unactive security turrets. Obviously you should destroy both turrets for more experience points.
Return to the previous room and approach a door on the northern wall. This will allow you to gain access to the room with a coil. There are two ways for you to collect the coil. A more dangerous solution will require you to use the upper balcony to jump inside the room with the electricity [#35]. You would then have to collect the object you were looking for, however you would receive MASSIVE injuries (or you could even die if you were playing as a weak character). As a result you should ignore this path and choose a better way to get your hands on the artifact.
Thankfully there's a much safer way for you to gain possession of the coil. Travel north and ignore the door leading out of the facility. Turn west and then south. Eventually you should be able to get to a small control room. Use a nearby computer terminal [#36]. Hacking into the system will allow you to disable the electricity. Proceed to the room with the coil and take it without any additional problems. Once this object is in your possession go back to the northern door leading back to Old Olney.
Sadly you won't be safe once you leave the facility, because you're going to be attacked by three deathclaws [#37] almost instantly. The beasts are very agile, so you wouldn't be able to outrun them. As a result choose a powerful weapon from your inventory and try to survive. Heal your character afterwards, open the world map and fast travel to the Citadel. Once you're there go to Citadel - A ring. Find Paladin Tristan and hand him over the coil. Listen to new orders from the brotherhood. You'll find out that you'll have to get to Adams Air Force Base using the Presidential Metro.