When you mean the northern part of a country, a region or the world, you can say the north or the North.
Birds are migrating from the north.
Houses are less expensive in the North than in the South.
Looking at the Corpus of the contemporary American English, I find 7 sentences containing a phrase similar to "12 degrees north of the equator"; in all of them north is not written capitalized, but one of them uses Equator instead of equator.
The Arecibo Observatory owes its existence largely to Puerto Rico's political status as a U.S. Commonwealth, and to its geographic position only 17 degrees north of the Equator.
Northern is an adjective, and it is not written capitalized, except when a word would be written capitalized, or when it is part of an official name, for example in Northern Ireland.