Why Electric eel doesn't electrifying itself ?
This is because the electric charge within the eel is greater than its surrounding environment, just as heat travels from an area of high concentration to an area of low concentration (when you touch a hot pan, you get burned, the pan does not), electric current generated by the eel's current-generating cells moves from the higher concentration (the eel) to a lower concentration (the prey). Moreover, the eel does not constantly produce electric current, it does so whenever it is needed for attacking, or when it is startled.
Fun fact: the Eel is not an eel, it is a knifefish! More clsoely related to the catfish.
Also, please remember that I'm making this answer up based on a wikipedia article and an intuitive guess. IF anyone can confirm or refute what I have said, I would be much obliged.
According to your explanation every "skin" cell of the eel have to be charged, as far as I know the voltage is created on some specific organ of the eel.
Ugh.... we covered this one afternoon in class. I forget the details, but IIRC it has to do with the discharge path out of the eel. Fat is electrically insulating, so it's possible to control how the current gets out. I think the skin is protective as well, but again, I forgot the details:
This reminds me of my high school chemistry days of osmosis, where in natural systems higher concentrations move to regions to lower concentration.
I guess this concept extends beyond biological systems.
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