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There is no such thing as an 'induced current'. What is 'induced' is a voltage. If the conductor into which that voltage is induced forms a complete circuit, then a current will result. But it's the voltage that's induced, NOT the current!

The direction of the induced voltage is explained by Lenz's Law which, in simple terms, tells us that the direction of the inducted voltage is always such that it will oppose the change in current that causes it. So the induced voltage will oppose any increase in current, but will act in the same direction as a reduction in current.

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Q: Who formulated a law for determining the direction of the induced current in a conductor?
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