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Induction An induced current is produced by a changing magnetic field There is an induced emf associated with the induced current A current can be produced without a battery present in the circuit Faraday’s law of induction describes the induced emf Faraday’s Experiment – Conclusions An electric current can be induced in a loop by a changing magnetic field This would be the current in the secondary circuit of this experimental set-up The induced current exists only while the magnetic field through the loop is changing Faraday’s law of induction states that “the emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit” dB ε dt Motional emf A motional emf is the emf induced in a conductor moving through a constant magnetic field The electrons in the conductor experience a force, F qv B that is directed along ℓ Sliding Conducting Bar A bar moving through a uniform field and the equivalent circuit diagram dB dx ε B B v The induced emf is dt dt Since the resistance in the circuit is R, the current is I ε R B v R Lenz’s Law Lenz’s law: the induced current in a loop is in the direction that creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop The induced current tends to keep the original magnetic flux through the circuit from changing Lenz’ Law, Example The conducting bar slides on the two fixed conducting rails The magnetic flux due to the external magnetic field through the enclosed area increases with time The induced current must produce a magnetic field out of the page If the bar moves in the opposite direction, the direction of the induced current will also be reversed Induced emf and Electric Fields The emf for any closed path can be expressed as the line integral of over the path Faraday’s law can be written in a general form: d B E ds dt This induced electric field is nonconservative