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The rule that gives the direction of induced current is called Lenz's Law.
A current is induced in a conductor whenever the magnetic flux through the region enclosed by the conductor is changing. The flux can change due to the change in magnitude or direction of the magnetic field, or due to the change of the area or orientation of the region enclosed by the conductor.
The Faraday's Law relates the emf induced in a conductor to the rate of change of the flux:
`Emf = -(dPhi)/(dt)`
The negative sign in the formula indicates that the induced emf will oppose the change of the flux. In other words, the magnetic field created by induced current will be in the opposite direction of the change. That is, if the flux is increasing, the induced magnetic field will be in the opposite direction of the original field. If the flux is decreasing, the induced magnetic field will be in the direction of the original field. Please see the reference link for the illustration.
The direction of the induced current can be determined by the right-hand rule, so that the induced current creates magnetic field in the direction opposite to the change.
So, the Lenz's Law states that the induced current will create induced magnetic field in the direction that will oppose the change of the magnetic flux.
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