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From last time…

From last time…. Faraday:. Changing flux generates EMF. Motional EMF. Moving conductor generates electric potential difference to cancel motional EMF. Motional EMF. Charges in metal feel magnetic force. Charges move, build up at ends of metal.

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From last time…

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  1. From last time… Faraday: Changing flux generates EMF Motional EMF Moving conductor generates electric potential difference to cancel motional EMF Physics 208, Lecture 19

  2. Motional EMF Charges in metal feel magnetic force Charges move, build up at ends of metal Equilibrium: electric force cancels magnetic force Physics 208, Lecture 18

  3. Question Two identical bars are moving through a vertical magnetic field. Bar (a) is moving vertically and bar (b) is moving horizontally. Which of following statements is true? A. motional emf exists for (a), but not (b) B. motional emf exists for (b), but not (a) C. motional emf exists for both (a) and (b) D. motional emf exists for neither (a) nor (b) Physics 208, Lecture 18

  4. Coil in magnetic field • Uniform B-field • increasing in time • Flux in z-direction increasing in time B(t) Induced current Lenz’ law: Induced EMF would produce current to oppose change in flux Physics 208, Lecture 19

  5. But no equilibrium current • Charges cannot flow out end • Build up at ends,makes Coulomb electric field • Cancels Faraday electric field • End result • No current flowing • Electric potential differencefrom one end to other • Opposes Faraday EMF • ΔV = - EMF - - - B(t) Increasing with time + + + Compare motional EMF Physics 208, Lecture 19

  6. N turns Surface for flux Wire turns Coil can generate it’s own flux • Uniform field inside solenoid • Change current -> change flux Physics 208, Lecture 19

  7. N=# of turns, =length of solenoid ‘Self’-flux in a solenoid Flux through one turn =Flux through entire solenoid inductance Physics 208, Lecture 19

  8. Inductance: a general result • Flux = (Inductance) X (Current) • Change in Flux = (Inductance) X (Change in Current) Physics 208, Lecture 19

  9. Question The current through a solenoid is doubled. The inductance of the solenoid Doubles Halves Stays the same Inductance is a geometrical property, like capacitance Physics 208, Lecture 19

  10. Question A solenoid is stretched to twice its length while keeping the same current and same cross-sectional area. The inductance Increases Decreases Stays the same Field, hence flux, have decreased for same current Physics 208, Lecture 19

  11. Fixed current through ideal inductor L • For fixed resistor value • Current through inductor I = Vbatt/R • Flux through inductor = LI • Constant current -> Flux through inductor doesn’t change • No induced EMF • Voltage across inductor = 0 I Vbatt R Ideal inductor: coil has zero resistance Physics 208, Lecture 19

  12. L Try to change current • You increase R in time: • Current through inductorstarts to decrease • Flux LI through inductor starts to decrease • Faraday electric fields in inductor wires • Induces current to oppose flux decrease • Drive charges to ends of inductor • Charges produce Coulomb electric field • Electric potential diff Va Vb I Vbatt R R(t) time Physics 208, Lecture 19

  13. Question The potential at a is higher than at b. Which of the following could be true? A) I is from a to b, steady B) I is from a to b, increasing C) I is from a to b, decreasing D) I is from b to a, increasing E) I is from b to a, decreasing e,.g. current from a to b: current increases, flux to right increases. sign of induced emf such that it would induce current to produce flux to left to oppose change in flux. Electric potential difference opposite to induced EMF, so Va>VB Physics 208, Lecture 19

  14. Energy stored in ideal inductor • Constant current (uniform charge motion) • No work required to move charge through inductor • Increasing current: • Work required to move charge across induced EMF • Energy is stored in inductor: • Total stored energy Energy stored in inductor Physics 208, Lecture 19

  15. Magnetic energy density • Energy stored in inductor • Solenoid inductance • Energy stored in solenoid Bsolenoid Energy density Physics 208, Lecture 19

  16. Question A solenoid is stretched to twice its length while keeping the same current and same cross-sectional area. The stored energy Increases Decreases Stays the same B decreases by 2 Energy density decr by 4 Volume increases by 2 Physics 208, Lecture 19

  17. Inductor circuit • Induced EMF extremely high • Breaks down air gap at switch • Air gap acts as resistor Physics 208, Lecture 19

  18. I Question • Here is a snapshot of an inductor circuit at a particular time. What is the behavior of the current? • Increasing • Decreasing • Nonzero Constant • Must be zero • Need more info Va Vb Physics 208, Lecture 19

  19. - I? + Perfect inductors in circuits • Constant current flowing • All Voltage drops = 0 I • Voltage needed to drive current thru resistor • -IR + VL = 0 Physics 208, Lecture 19

  20. - I? + RL circuits • Current decreases in time • Slow for large inductance • (inductor fights hard, tries to keep constant current) • Slow for small resistance • (little inductor voltage needed to drive current) • Time constant Physics 208, Lecture 19

  21. RL circuits - • Time constant I(t) + Physics 208, Lecture 19

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