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27. Electromagnetic Induction

27. Electromagnetic Induction. Topics. Magnetic Flux Faraday’s & Lenz’s Laws Inductance Magnetic Energy. Magnetic Flux. The magnetic flux through a surface is defined by. In the 1830s, Michael Faraday and Joseph Henry discovered that a changing magnetic flux can induce currents.

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27. Electromagnetic Induction

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  1. 27. Electromagnetic Induction

  2. Topics • Magnetic Flux • Faraday’s & Lenz’s Laws • Inductance • Magnetic Energy

  3. Magnetic Flux The magnetic flux through a surface is defined by In the 1830s, Michael Faraday and Joseph Henry discovered that a changing magnetic flux can induce currents

  4. Magnetic Flux The unit of magnetic flux is T m2, that is, a weber (Wb) Usually, an engineer is interested in the flux through a surface bounded by a wire

  5. Magnetic Flux For a constant magnetic field, the flux through a wire loop of area A is

  6. Magnetic Flux For N loops of wire, and a constant magnetic field, the flux is N times greater; that is, it is

  7. Faraday’s Law Faraday and Henry discovered that a changing magnetic flux through a wire loop creates an electric field within the loop, which induces an emf (a potential difference) in the wire

  8. Faraday’s Law The experimental observations can be summarized in the following law Faraday’s Law

  9. Lenz’s Law The induced emf is such as to oppose the change that produces it

  10. Lenz’s Law B2 is the magnetic field caused by current induced in the wire. By Lenz’s law, the induced magnetic field acts in a direction opposite the changing magnetic field B1

  11. Lenz’s Law We use the right-hand rule to determine the direction of the current I

  12. Example: Induced emf A conductor moving through a magnetic field will have an electric field induced in it, given byqE = q v B, that is, E = v B

  13. Example: Induced emf The induced potential difference is then DV = E l = v B l, once the current stops.

  14. Inductance The magnetic flux through a coil is proportional to the current flowing through it, so we can write The proportionality constant L is called the self-inductanceof the coil, whose unit is the henry (H = 1 Wb/A )

  15. Inductance Example: self-inductance of a long solenoid that is,

  16. Inductance Consider a changing magnetic flux through a coil But, since we find a self-induced emf of

  17. Magnetic Energy Consider a circuit containing a resistor R and a coil of self-inductance L. From Kirchoff’s loop rule, we can write

  18. Magnetic Energy Multiply throughout by I and re-arrange battery power joule heating power in coil

  19. Magnetic Energy Therefore, the energy stored in the inductor (the coil in this case) is found by integrating the power in the coil with respect to time

  20. CMS @ CERN

  21. The CMS Solenoid Magnet

  22. Magnetic Energy – CMS The magnetic field of a solenoid is For CMS B = 4 T I = 20,000 A l = 12.5 m r = 3 m

  23. Magnetic Energy – CMS The energy stored in the CMS solenoid is given by For CMS B = 4 T I = 20,000 A l = 12.5 m r = 3 m This is enough to melt 18 tons of gold!

  24. Magnetic Energy In general, the energy density in a magnetic field is given by

  25. Summary • Faraday’s law • A changing magnetic flux induces an electric field. • In a circuit, the induced electric field induces an emf and an induced current. • Lenz’s law • The induced current is such that the magnetic field it produces acts to oppose the change that gives rise to it.

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