I've had a cactus since December, which is placed next to a Northern facing window. I've only watered it a handful of times since then. It has a small piece near the top which about 2 weeks ago turned light green, then brown and is now shriveled. The rest of the cactus seems fine. Can someone please tell me what the cause of this is? Is the cactus generally in good health or should I be worried that the rest of it will turn out this way?
I see two issues. A. a northern facing window is not going to provide sufficient light for healthy growth. B. your plant is very dehydrated. It's not in active growth and should be at this time of year (assuming northern hemisphere). When the top inch of soil is dry water until the water runs out the drains in the pot.
As far as what caused the pad to turn brown and die, it's hard to tell from the photos. You should grab the bad looking pad with tongs or a paper towel (double or tripled over) and use a sharp knife to cut right at the attachment to the rest of the plant.