I've read on the Internet that wearing plastic shoes doesn't allow electric charges we collect from our environment (PC, TV, appliances) to be earthed.
Is this reasoning correct?
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Yes, the reasoning is correct as long as electric potential you're touching isn't very-very high and the plastic is normal (Conductor plastic has been invented).
Electricity flows from higher potential to lower potential via a conductor. Earth is zero potential and Human body is a good conductor which allows electricity flow when we touch anything at positive potential with naked feet. Normal plastic, rubber etc are bad conductor of electricity which disconnects higher potential from lower one. But, remember, a bad conductor can't hold if potential difference is very high (meaning, the point you're touching has very-very high potential).