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Clicker Question: Non-uniform B field

Clicker Question: Non-uniform B field. A current loop is oriented so that its magnetic dipole is oriented along direction “2”. In which direction is the force on the loop?. In direction 1 In direction 2 In direction 3 In direction 4 No force. Maxwell’s Equations (incomplete).

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Clicker Question: Non-uniform B field

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  1. Clicker Question: Non-uniform B field A current loop is oriented so that its magnetic dipole is oriented along direction “2”. In which direction is the force on the loop? • In direction 1 • In direction 2 • In direction 3 • In direction 4 • No force

  2. Maxwell’s Equations (incomplete) Gauss’s law for electricity Gauss’s law for magnetism Incomplete version of Faraday’s law Ampere’s law (Incomplete Ampere-Maxwell law) First two: integrals over a surface Second two: integrals along a path Incomplete: no time dependence

  3. Chapter 23 Faraday’s Law

  4. Changing Magnetic Field Solenoid:inside outside Constant current: there will be no forces on charges outside (B=0, E=0) What if current is not constant in time? Let B increase in time E~dB/dt E~1/r Non-Coulomb ENC !

  5. Two Ways to Produce Electric Field 1. Coulomb electric field:produced by charges Same effect on charges: 2. Non-Coulomb electric field: using changing magnetic field Field outside of solenoid

  6. Direction of the Curly Electric Field Right hand rule: Thumb in direction of fingers: ENC Exercise: Magnetic field points down from the ceiling and is increasing. What is the direction of E?

  7. Driving Current by Changing B ENC causes current to run along the ring What is the surface charge distribution? What is emf and I? Ring has resistance, R

  8. Effect of the Ring Geometry 1. Change radius r2 by a factor of 2. emf does not depend on radius of the ring! 2. One can easily show that emf will be the same for any circuit surrounding the solenoid

  9. Round-Trip Not Encircling the Solenoid =0 =0 _ + for any path not Enclosing solenoid!

  10. Exercise Is there current in these circuits?

  11. Quantitative Relationship Between B and EMF Can observe experimentally: I=emf/R ENC~emf • ENC~dB/dt • ENC~ cross-section of a solenoid

  12. Magnetic Flux - magnetic flux mag on the area encircled by the circuit Definition of magnetic flux: Magnetic flux on a small area A: This area does not enclose a volume!

  13. Faraday’s Law Michael Faraday (1791 - 1867) Faraday’s law cannot be derived from the other fundamental principles we have studied Formal version of Faraday’s law: Sign: given by right hand rule

  14. Including Coulomb Electric Field =0 Can we use total E in Faraday’s law?

  15. A Circuit Surrounding a Solenoid Example: B1 changes from 0.1 to 0.7 T in 0.2 seconds; area=3 cm2. V What is the ammeter reading? (resistance of ammeter+wire is 0.5) V downwards

  16. A Circuit Not Surrounding a Solenoid If we increase current through solenoid what will be ammeter reading?

  17. The EMF for a Coil With Multiple Loops Each loop is subject to similar magnetic field  emf of loops in series:

  18. Moving Coils or Magnets by moving magnet: by rotating magnet: (or coil) Time varying B can be produced by moving coil:

  19. Exercise 1. A bar magnet is moved toward a coil. What is the ammeter reading (+/-)? + 2. The bar magnet is moved away from the coil. What will ammeter read? _ 3. The bar magnet is rotated. What will ammeter read? _ ?

  20. Faraday’s Law and Motional EMF I I ‘Magnetic force’ approach: Use Faraday law:

  21. Example R L v I B1 B2 Lvt

  22. Faraday’s Law and Generator I

  23. Two Ways to Produce Changing  Two ways to produce curly electric field: 1. Changing B 2. Changing A

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