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Charging by induction seems very unintuitive to me. Let me explain:

Consider a positively charged rod and a neutrally charged conductor. You can charge it by induction by earthing it and not lose charge on the rod. You can then use this potential difference in the spherical conductor as energy. This can be repeated many times. Does this not violate the law of conservation of energy?

Also, why does charging by friction work? Consider conductors $A$ and $B$, which I charge by rubbing together. Assume that $A$ gains electrons during the charging process and $B$ loses them. But, as soon as $A$ gains an electron, that electron should move back to $B$, since we have a potential difference and a path for conduction.

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As far as I am aware, charging by friction occurs between insulators.

In this situation, friction allows a charge to build up due to the energy provided by friction itself (kinetic energy). When energy is being applied, the charge builds up, and when energy ceases to be applied, the potential difference remains as the charges are stored within the insulators - there is no path for conduction.

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You can then use this potential difference in the spherical conductor as energy. This can be repeated many times. Does this not violate the law of conservation of energy?

Conservation of energy applies to closed systems. If you connect your conductor to the ground, it is no longer a closed system of its own.

Also, as has already been mentioned in the other answer, there is no electrical conduction between the two materials.

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