Different metals have more or less electrons in their atoms. When two different metals contact, the difference in electrons create difference of potential (galvonic reaction), This difference of potential causes corrosion (corrosion). The idea is to connect a sacrificial anode and apply a voltage of opposite polarity causing a cancellation of the galvonic reaction. If you can cancel the voltage difference you stop the corrosion. If some of the voltage remains the anode will be used up instead of the base metal your trying to protect.. Yes it works. You don't need to be grounded to the Earth, ground is a reference.
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Sorry, but as you guessed, they're a scam.Sacrificial anodes do work pretty well on boats, because the boat is immersed in a conductive medium (water) which is all at the same electrical potential, so you can use electricity to more-or-less direct the current to a point you're willing to have worn away and away from the rest. However, if your car is ever immersed, you have bigger problems than rust... and if it isn't, than the most a sacrificial anode might _possibly_ do is protect the area right near it -- and that only while that area stays wet.In any case, modern cars are made out of metals which are significantly more rust-resistant than older vehicles -- and these days are often using plastics for the thinner pieces where corrosion might be more of an issue -- so in general you really shouldn't be spending too much time, effort, or money worrying about the issue. Even in the snow belt, a car can easily go a decade before there's enough rust to even be a cosmetic issue.If you insist on worrying, the best thing you can do is *NOT* to garage your car during winter. Really. The reaction between salt and metal is slowed down by cold. Combine that with frequent car washes (think of how many washes the price of that electronic gizmo will pay for) and you're good to go.