Electric charges are easily visible to human eyes, even though their motion is not. "Electricity" is not invisible! Never has been. When you look at a metal wire, you can see the charges of electricity which would flow during electric currents. They are silvery/metallic in color. They give metals their mirrorlike shine. Some metals have other colors as well, brass and copper for instance. Yet in all cases, the "metallic"-looking stuff is the metal's electrons. A dense crowd of electrons looks silvery; "electric fluid" is a silver liquid. And if metals weren't full of movable electrons, they wouldn't look metallic.
During electric currents in metals, the atoms stay still, but the silvery electron-stuff flows slowly along. Unfortunately the human eye cannot see the electric flow. That's part of the reason that "electricity" is so mysterious. Think about it... in an aquarium full of water, you cannot see any water flowing unless there are bubbles or dirt being carried along. And whenever clean water is flowing through a transparent hose, you can't see any flow. Even if the water is flowing very fast, the water-filled hose just looks like an unmoving glass rod. Same with wires: there's no bubbles or dirt being carried along by the electric current, therefore you can't see anything moving. You can see the STUFF that flows, just as you can see the water in an aquarium, but you can't see any flowing stuff.
Even if human eyes could see single electrons, we still couldn't see an electrical flow since the current is extremely slow. Electrons in metals typically flow at a few centimeters per hour, even during high currents. That's slower than the minute hand on a clock! Electric currents OOZE along like silly-putty flowing across a tilted board.
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Seeing imbalances in charge
Here's a separate topic... while the metallic-looking sea of charges in a metal is easily seen, IMBALANCES of charge are not. This get's confusing, since many books call imbalances of charge by the name "charge." They will tell you that charge is invisible, yet they really mean that charge-imbalances are invisible.
Wires contain enormous amounts of movable negative charge in the form of electrons, but they also contain positive charge in the form of protons within the metal atoms. If the number of protons and electrons are equal, don't they cancel out? Doesn't that mean that no charge exists? No. It means that no IMBALANCE of charge exists.
An "uncharged" wire is still full of charge, it still contains positive and negative charge in huge but equal quantities. The word "uncharged" doesn't mean "without charge," instead it means "without charge-imbalance." Yet even if there are more electrons than protons, or fewer electrons than protons, this imbalance is invisible. It's invisible because the greatest difference attainable is incredibly tiny when compared to the amount of charge that's already there. If an object is highly charged; even charged up to millions of volts, the extra charge is like a teacup poured into an ocean. The difference is far too small to be seen.
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