Chemistry isn't the place to go, head for the physiology section of your library or go to the med school library. Nerve fibers "depolarize" just like muscle fibers; there's an inrush of sodium ions radially inward across the fiber membrane that changes the relative potential of inside versus outside. This propagates down the axon (think cylinder) away from the bulk of the cell body. There's a strong electric field between the depolarized portion and the polarized (resting) downstream part that then triggers the downstream part of the membrane to depolarize, thus propagating the signal further. People have used the EE's telegraphy equation (transmission line) to model the propagation. As you read, you'll learn about the sodium pump, the role of the myelin sheath in speeding up propagation, and other amazing stuff. Hodgkin and Huxley won a Nobel for figuring out the basics.
The propagating ionic "wave" represents a current flow and generates electric fields that cause potential differences at the skin. In the brain, we measure them as the EEG. They're weak, both because of the smallness of the current and the fact that it flows in physically small loops that are seen from a great distance. You can also pick up extremely weak magnetic signals, the MEG; they have the advantage of good localization ("direction finding") since the field is directly related to the source without the conduction and smearing through intervening tissue that affects the EEG.
I don't have any good references for you, it's been decades since I worked in this area, but physiology texts will cover the cellular processes, and neurology/neurobiology texts will give you more. Later if you want an entry into the physics literature, I would try searching on things like action potential propagation, nerve current propagation, magnetoencephalogram, etc. Take a look in articles for references either to textbooks and review articles, or to early literature where they were figuring out the basics.
Don't make up your mind on accelerators until you look into this. It's pretty cool!
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