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From last time…

Learn about magnetic flux, Faraday's law, and how time-varying magnetic fields create electric fields. Explore the concepts through examples and quizzes.

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From last time…

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  1. From last time… dB r dI Magnetic field generated by current element: Biot-Savart Magnetic flux

  2. Average = 64% B BC AB C A D Physics 208, Lecture 17

  3. Magnetic flux • Magnetic flux is defined as • (Component of B  surface) x (Area element) zero flux Maximum flux SI unit of magnetic flux is the Weber ( = 1 T-m2 ) Physics 208, Lecture 17

  4. Magnetic Flux • Magnetic flux  through a surface: (component of B-field  surface) X (surface area) • Proportional to # B- field lines penetrating surface Physics 208, Lecture 17

  5. A magnetic flux analogy Physics 208, Lecture 17

  6. Question A ring of 1m cross-sectional area makes an angle of θ=60˚ with respect a 2T magnetic field. The magnetic flux through the ring is • 0.2 Weber • 0.5 Weber • 1.0 Weber • 2.0 Weber • 5.0 Weber Uniform field gives Physics 208, Lecture 17

  7. Time-dependent fields • Up to this point, have discussed only magnetic and electric fields constant in time. • E-fields arise from charges • B-fields arise from moving charges (currents) Faraday’s discovery • Another source of electric field • Time-varying magnetic field creates electric field Physics 208, Lecture 17

  8. Measuring the induced field • A changing magnetic flux produces an EMF around the closed path. • How to measure this? • Use a real loop of wire for the closed path. The EMF corresponds to a current flow: Physics 208, Lecture 17

  9. Nonuniform field from bar magnet • Moving the magnet changes flux through the ring. • Faraday effect predicts electric field in loop, which drives a current. Physics 208, Lecture 17

  10. N Question Which direction of motion does NOT induce a current in loop? W E • North • East • West • NorthEast S Physics 208, Lecture 17

  11. Current but no battery? • Electric currents require a battery (EMF) • Faraday: Time-varying magnetic field creates EMF Faraday’s law: EMF around loop = - rate of change of mag. flux Physics 208, Lecture 17

  12. + Electric potential difference • Work/charge to move charge against electric forces d b a + Example uniform electric field Electric force on charge q Work to move particle as shown Electric potential difference Physics 208, Lecture 17

  13. + Electric fields from charges • Uniform E-field can arise from infinite charge sheet + These are called “Coulomb” electric fields They are produced by charges Physics 208, Lecture 17

  14. Question This electric field line could be generated by • Point charge • Dipole charge • Plane of charge • Ring of charge • None of these Physics 208, Lecture 17

  15. Making E-field by Faraday’s method Physics 208, Lecture 17

  16. Different ways to make E-field Coulomb electric field Created by electric charges Non-Coulomb electric field Created by time-varying magnetic field Physics 208, Lecture 17

  17. Question Faraday E-field You move a positive charge counterclockwise all the way around the circular path, returning to your starting point. The work you have done is • Positive • Negative • Zero Physics 208, Lecture 17

  18. EMF in a circuit, or along a path Work done by E-field = So is work per unit charge to bring charge back to where it started. This is zero. Physics 208, Lecture 17

  19. Faraday’s law EMF around loop Magnetic flux through surface bounded by path EMF no longer zero around closed loop Physics 208, Lecture 17

  20. Quick quiz Which of these conducting loops will have currents flowing in them? B. A. I(t) increases Constant I D. C. Constant v Constant v Constant I Constant I Physics 208, Lecture 17

  21. Faraday’s law • Faraday’s law • Time-varying B-field creates E-field • Conductor: E-field creates electric current • Biot-Savart law • Electric current creates magnetic field • Result • Another magnetic field created Physics 208, Lecture 17

  22. Lenz’s law • Induced current produces a magnetic field. • Interacts with bar magnet just as another bar magnet • Lenz’s law • Induced current generates a magnetic field that tries to cancel the change in the flux. • Here flux through loop due to bar magnet is increasing. Induced current produces flux to left. • Force on bar magnet is to left. Physics 208, Lecture 17

  23. Quick quiz What direction force do I feel due to Lenz’ law when I push the magnet down? Up Down Left Right Strong magnet Copper Physics 208, Lecture 17

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