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Chapter 30 Faraday’s Law

Main Points of Chapter 30 Magnetic induction Induced current and Lenz’s law Motional emf Eddy currents Induced electric fields Generators

30-1 Faraday’s Discovery and the Law of Induction Faraday wanted to know if magnetic fields would create electric fields Steady fields did not But changing fields did!

30-1 Faraday’s Discovery and the Law of Induction There are many ways to change the magnetic flux through a surface: Move the magnet Turning current on or off in one loop induces current in another Move the loop Change the shape (and the area) of the loop

30-1 Faraday’s Discovery and the Law of Induction A changing magnetic flux through a loop induces a current around the loop Faraday’s law of induction: (30-2)

30-1 Faraday’s Discovery and the Law of Induction The direction of the induced current is given by Lenz’s law: The induced current is in a direction such that the magnetic field it creates tends to oppose the change that created it If it were in the other direction, energy would not be conserved

30-2 Motional emf Created by a conductor moving in a magnetic field “Loop” is imaginary but real emf is induced in conductor

30-2 Motional emf Motional emf: (30-5) Eddy currents: produced in conductor moving in magnetic field Can make a very effective brake If you don’t want a brake, eddy currents can be foiled by cutting holes (slots) in conductor

30-3 Forces and Energy in Motional emf Consider loop moving from region of constant magnetic field into region of no magnetic field. Flux changes as loop crosses boundary. Force tends to slow loop down (drag force) Magnitude of force: (30-8)

30-4 Time-Varying Magnetic Fields A changing magnetic field induces an electric field Electric field can be calculated given sufficient symmetry

30-5 Generators An external force rotates a loop in a magnetic field An emf is induced: Induced power: (30-14) (30-16, 18)

30-5 Generators The sinusoidally varying current and voltage are characteristic of electricity from generators Electricity from batteries is constant

Summary of Chapter 30 Faraday’s law: A changing magnetic flux induces an emf: (30-2) Lenz’s law: Induced currents produce magnetic fields that tend to cancel the flux changes that induce them. Motional emf is induced when conductor moves through magnetic field