You chose to bid 2 Spades. This is the correct bid. You have a nice 5 card Spade suit, and you have over 10 points, so you must jump bid to indicate this to your partner, in case s/he has aspirations for a game bid.

Now it is time for West to bid again. Since his partner did not bid, he will not rebid.

And now it is time for North to reconsider whether to rebid or not. If his partner had bid 1 Spade, he certainly would not have rebid, but would have left his partner in that bid. However, his partner is inviting him to go to game, if he is strong enough.  Knowing he has a Spade fit with his partner, means he can upgrade his point count with short-suit points for his singleton, bringing it up to 18. He can expect his partner to have at least 10 points to have given him a jump response.

Spades         J,8,3,2
Hearts         A
Diamonds    K,Q,8,4
Clubs          K,Q,8,4

39. What rebid should North now make?

a. No Bid
b. 3 No Trump
c. 4 Spades