This is a Frame Challenge
You appear to be setting the size of the organ without first deciding how the organ operates. Unless you have a reason for such a large organ that you've not explained, deciding its size before deciding its operation is putting the cart before the horse.
Similarly, you're thinking in terms of one organ. However, given the brief description of what you want that organ to achieve, it makes more sense to have multiple organs.
You mention that it's an "electric organ" and that's likely leading people to make some assumptions. However, I'd like to point out that while electricity (in the form of the human nervous system) might be involved, the organ itself is not electric. It's magnetic. In fact, I think in your case it would help that you avoid the idea of an electromagnet and even avoid the idea of an electrically conductive ferro magnet and stick with the idea of an electrically non-conductive ferrite magnet, which is more along the lines of what a biological solution would be anyway.
What I think you might consider
It's important to work though what you expect your characters to do with this ability before you design the rationalization for its existence (create the organ).
Let's say there is only one organ, that the organ generates magnetism, and that it's located within the sacrum, the bone at the bottom of the spine. What could you do with it? You could be the all-time world-champion of musical chairs, at least as long as the chairs are made of a ferrous metal. And you could, um... redirect explosive objects by running away from them. I just don't see a lot of practical here. If it's strong enough it could disrupt communications... something like an
EM fart EMP, dontchaknow.
But... let's put something in the palm of each hand. Now we have something we can work with. That helps the person climb and hang onto things. It simulates telekinesis. And it can do everything I just mentioned if it were located in the sacrum.
But you have two hands... makes sense you have two organs. In fact, it makes sense that you have three. The two emitters in the hands, and the "control organ" that creates the enzymes/proteins/juju necessary for the two emitters to work.
OK, so where and what size?
Now that we know a bit more about the whats and why, we can address the where. The organs in the hands shouldn't affect how hands are used already — at least not to a great degree. I'm voting for a spot between the second and third metacarpus bones This organ wants to be small, the size of a cashew at most, but it will need to be hard (from a fleshy perspective) to rationalize what it's doing.
Does that matter? Of course not. People born with this organ wouldn't even know it's there. They would have been training from birth to simply deal with it. They wouldn't notice it any more than they notice their kidneys... unless someone hits them in the kidneys. Interesting aspect for your story, no?
The "controlling organ" wants to be in the brain where it's close to the action. I don't think it needs to be too terribly large, either. Maybe the size of a small grape or an M&M. But I'm thinking to tuck it in with the Thalamus, which is the "body's information relay station."
Now, you might have had a reason for the large organ...
This is why my frame challenge exists. You might have a worldbuilding reason for the large organ that you haven't told us. If you do, that reason is important and we need to know it. If you don't, or if the reason is story-based rather than worldbuilding, then I invite you to reconsider the design of your organ(s).
But, let's assume that we absolutely must have a 15cm organ. Just for the record, an average finger length (index or middle finger) is about 11cm and the average human heart is 12cm tall - so you're talking about an organ that's longer than the average human heart or average index finger. That's huge and the only practical place it can go is to replace the appendix or, perhaps, to slide it between the stomach and intestines. There isn't a lot of free space in the human body (as long as you ignore body fat) and that organ is absolutely enormous. Which is why I'm advocating redesigning it.