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Electromagnetic Induction Basic Concepts Faraday’s Law (changing magnetic flux induces emf) Lenz’s Law (direction of induced current) Motional emf Physics 24-Winter 2003-L18 1 Two Experiments • Experiment 1: Conducting Coil and Magnet • Experiment 2: Pair of Conducting Coils Physics 24-Winter 2003-L18 2 Two Experiments Induced current and induced emf when something changes. What is it? Faraday: An emf is induced in the coil when the number of magnetic field lines that pass through the coil is changing. How to determine the amount of magnetic field lines that pass through a coil? Physics 24-Winter 2003-L18 3 Faraday’s Law of Induction The emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit: dB dt If the circuit contains N loops all with the same area an emf is induced in every loop, and the total induced emf is dB N dt Physics 24-Winter 2003-L18 4 Ways to Change the Magnetic Flux dB dt B dB N dt • Change the magnetic field within the coil • Change the area of the coil in the field (for example, stretch the coil or move it in or out of the field) • Change the angle between the magnetic field direction and the coil (rotate the coil) Physics 24-Winter 2003-L18 5 Some Applications of Faraday’s Law • • • • • • Ground Fault Interruptors (GFI) Electric Guitar Pickup Coils Alternators Generators Phonograph Cartridges Magnetic Tape Readers Physics 24-Winter 2003-L18 6 Direction of Induced emf dB N dt What about that pesky minus sign? An induced emf produces a current that creates a magnetic flux to oppose the original change in the magnetic flux. This is known as Lenz’s Law Physics 24-Winter 2003-L18 7 Examples of Lenz’s Law Determine the direction of the induced current in each resistor below. 1. I I 3. 2. I I suddenly decreases. Physics 24-Winter 2003-L18 8 Motional emf Motional emf is the emf induced in a conductor moving in a magnetic field. We will limit this to constant magnetic fields. The magnetic force on the electrons in the + bar causes them to move downward. E v B l FB qv B ev B This separates the charges in the bar producing an electric field in the bar. The electric field exerts an upward force on the electrons. FE qE eE At equilibrium the forces balance, and FB FE 0 e E evB Physics 24-Winter 2003-L18 9 Motional emf + E v B l The separation of charges also produces a voltage difference across the bar, or an induced emf, . El Since e E evB we can write El Blv or Blv When a conductor moves through a uniform magnetic field a potential difference is maintained between the ends of the conductor. Physics 24-Winter 2003-L18 10 Motional emf l R v F ap p I B x A more interesting situation occurs when the moving bar is part of a closed conducting path. We assume the bar has zero resistance, and that the stationary part of the circuit has resistance R. As the bar is pulled to the right with velocity v by the applied force Fapp the electrons are again subject to a downward force. Now, however, the electrons are free to move in the closed conducting path and a counterclockwise current is established. Physics 24-Winter 2003-L18 11 Motional emf l R v F ap p I B x Does the induced counterclockwise current follow Lenz’s law? As the bar slides to the right the magnetic flux through the circuit into the page is increasing. Lenz’s law says the induced current will produce a magnetic field to oppose that increase. In other words, the induced current should produce a magnetic field that points out of the page. A counterclockwise current does this. Physics 24-Winter 2003-L18 12 Motional emf l R v F ap p I B x The magnetic flux through the circuit at this instant is B = BA = Blx. So Faraday’s law gives the following: dB d dx Blx Bl Blv dt dt dt Hence Blv I R R Physics 24-Winter 2003-L18 13 Motional emf l R v F F B ap p I B x As the bar moves through the uniform magnetic field B it also experiences a magnetic force FB. FB Il B This force is opposite the applied force and because the bar moves with constant velocity it must be equal in magnitude as well. Fapp FB IlB Physics 24-Winter 2003-L18 14 Motional emf l R v F F B ap p I Fapp FB IlB B x The power supplied by the applied force is then P Fappv IlB v Blv Since we found I then P IlB v I Blv I 2 R R First the mechanical energy is converted to electrical energy. This electrical energy is then converted to internal energy in the resistor. Physics 24-Winter 2003-L18 15