The neatest way of doing it is to take the wire across the attic side of the ceiling. If there is a floor above, then there is a bit of carpentry involved. Determine which way the ceiling joists run and open a hole between them and fish the wire to the new location where it is needed. There is also in the market place a product called Wiremold. It is a surface conduit system.
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A jumper wire should use to bridge electrical ground across?
No, you can feed it with a 2 wire Romex + ground. It depends on what is mounted on the ceiling. If it is just a light all you need is 2 wire + ground Romex. However if it is a fan/light and you want to control each one independant of the other you will need to use 3 wire Romex + ground. This is of course if you have 2 seperate switches. You would then connect the red wire to the blue light wire and the black wire to the black fan wire. If you use 2 wire Romex just connect the blue and black fan/light wire to the black wire in the ceiling box.
The neutral wire will have writing or ribs on it and connects to the white wire. The smooth wire is hot and connects to the black wire. Use 3 strand wire in size AWG # 16. If the fan has a light it will have a blue wire. Connect that blue wire to the black wire.
the hot wire carries the electrical voltage
It could be anywhere from 36 to 48SWG