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The story so far…

The story so far…. d B. r. d I. Magnetic field generated by current element: Biot-Savart. I. Ampere’s law. closed path. surface bounded by path. Exam 2 results. Grade cutoffs: A: 86 AB: 79 B: 66 BC: 58 C: 37 D: 23. Ave=69. Ampere’s law. Sum up component of B around path

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The story so far…

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  1. The story so far… dB r dI Magnetic field generated by current element: Biot-Savart I Ampere’s law closed path surface bounded by path

  2. Exam 2 results Grade cutoffs: A: 86 AB: 79 B: 66 BC: 58 C: 37 D: 23 Ave=69 Physics 208, Lecture 18

  3. Ampere’s law Sum up component of B around path Equals current through surface. Component of B along path I closed path • Ampere’s law surface bounded by path Physics 208, Lecture 18

  4. “Ampere’s law” in electrostatics 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 18

  5. Gauss’ law in electrostatics • Electric flux through surface  charge enclosed What about magnetic flux? Physics 208, Lecture 18

  6. Magnetic flux • Magnetic flux is defined exactly as electric flux • (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 18

  7. Magnetic flux What is that magnetic flux through this surface? Positive Negative Zero Physics 208, Lecture 18

  8. Gauss’ law in magnetostatics • Net magnetic flux through any closed surface is always zero: Compare to Gauss’ law for electric field No magnetic ‘charge’, so right-hand side=0 for mag. Basic magnetic element is the dipole Physics 208, Lecture 18

  9. Comparison with electrostatics Gauss’ law Ampere’s law Electrostatics Magnetostatics Physics 208, Lecture 18

  10. 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 18

  11. 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 18

  12. 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 18

  13. Faraday’s law EMF around loop Magnetic flux through surface bounded by path EMF no longer zero around closed loop Physics 208, Lecture 18

  14. Quick quiz Which of these conducting loops will have currents flowing in them? I(t) increases Constant I Constant v Constant v Constant I Constant I Physics 208, Lecture 18

  15. 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 18

  16. 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 18

  17. 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 18

  18. Quick Quiz • A conducting rectangular loop moves with constant velocity v in the +x direction through a region of constant magnetic field B in the -z direction as shown. • What is the direction of the induced loop current? CCW CW No induced current y x Physics 208, Lecture 18

  19. Quick Quiz • Conducting rectangular loop moves with constant velocity v in the -y direction away from a wire with a constant current I as shown. What is the direction of the induced loop current? I CCW CW No induced current v B-field from wire into page at loopLoop moves to region of smaller B, so flux decreasesInduced loop current opposes this change, so must create a field in same direction as field from wire -> CW current. Physics 208, Lecture 18

  20. L - Motional EMF • Conductor moving in uniform magnetic field • + / - charges in conductor are moving. • Magnetic field exerts force. Charges pile up at ends Static equilibrium: E-field generated canceling magnetic force Solid conductor Physics 208, Lecture 18

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