Ah, electricity! What a shocker!
And, no, I'm not talking about that "spark" between you and that special someone. I'm talking about that raw flow of electrons that's oh so important to the world today. Where did that all begin?
William Gilbert, an astronomer, is generally considered the first electrical engineer because of his invention of the first electroscope, a device he called the versorium, all the way back in 1600. It was pretty simple, actually, a needle that detected static charges.
So, these days, a good education is the key to becoming an electrical engineer. You just go and get a degree in it. Education is never a bad thing. However, it's not a field that's limited to your education. There is still plenty we don't know, especially considering that we can't reproduce many of the things we know Tesla could do and have absolutely no idea about some of the things he claimed to be able to do. Heck, for all we know, he and his buddy Mark Twain were zipping around in a time machine.
The point is this, almost everything you own uses electricity. Even some of the books. Electrical engineering is not a static field (heh heh, get it?). It's definitely the kind of place where bright people with an eye to the future and all of the possibilities therein would want to be. So, yes, go to school, get a degree, learn all you can, but, then, get out there and experiment. Electrical engineering is wide and diverse field.