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From last time… Faraday: d B dt Changing flux generates EMF Motional EMF Moving conductor generates electric potential difference to cancel motional EMF Thur. Nov. 5, 2009 Physics 208, Lecture 19 1 Motional EMF Charges in metal feel magnetic r r force qv B Charges move, build up at ends of metal r r FE FB qE qV /l qvB Tue. Nov. 2, 2009 Equilibrium: electric force cancels magnetic force so V vl B Physics 208, Lecture 18 2 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) Tue. Nov. 2, 2009 Physics 208, Lecture 18 3 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 Thur. Nov. 5, 2009 Physics 208, Lecture 19 4 But no equilibrium current Charges cannot flow out end Build up at ends, makes Coulomb electric field Cancels Faraday electric field - -B(t) +++ Increasing with time End result No current flowing Electric potential difference from one end to other Opposes Faraday EMF ΔV = - EMF Thur. Nov. 5, 2009 Compare motional EMF Physics 208, Lecture 19 5 Coil can generate it’s own flux Uniform field inside solenoid Binside Change current -> change flux o N I N turns Wire turns Thur. Nov. 5, 2009 Surface for flux Physics 208, Lecture 19 6 ‘Self’-flux in a solenoid Bsolenoid oN I N=# of turns, =length of solenoid o NA I Flux through one turn Bsolenoid A o N 2 A I =Flux through entire solenoid NBsolenoid A inductance LI Lsolenoid o N 2 A / Thur. Nov. 5, 2009 Physics 208, Lecture 19 7 Inductance: a general result Flux = (Inductance) X (Current) LI Change in Flux = (Inductance) X (Change in Current) LI Thur. Nov. 5, 2009 Physics 208, Lecture 19 8 Question The current through a solenoid is doubled. The inductance of the solenoid A. Doubles B. Halves C. Stays the same Inductance is a geometrical property, like capacitance Thur. Nov. 5, 2009 Physics 208, Lecture 19 9 Question A solenoid is stretched to twice its length while keeping the same current and same cross-sectional area. The inductance Bsolenoid A. Increases B. Decreases C. Stays the same oNI Field, hence flux, have decreased for same current LI Lsolenoid o N A / 2 Thur. Nov. 5, 2009 Physics 208, Lecture 19 10 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 Thur. Nov. 5, 2009 Physics 208, Lecture 19 11 L Try to change current You increase R in time: Current through inductor starts to decrease Vb Flux LI through inductor starts to decrease Faraday electric fields in inductor wires R Va I Vbatt Induces current to oppose flux decrease Drive charges to ends of inductor R(t) Charges produce Coulomb electric field dI Electric potential diff VL Vb Va L Thur. Nov. 5, 2009 time dt Physics 208, Lecture 19 12 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 Thur. Nov. 5, 2009 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 13 Energy stored in ideal inductor Constant current (uniform charge motion) No work required to move charge through inductor Increasing current: Work VLq VL Idt required to move charge across induced EMF dI dW V Idt L Idt LIdI L dt Energy is stored in inductor: dUL dW Total stored energy UL I 0 Thur. Nov. 5, 2009 1 2 Energy stored LIdI LI in inductor 2 Physics 208, Lecture 19 14 Magnetic energy density 1 2 Energy stored in inductor UL LI 2 N 2A Solenoid inductance Lsolenoid o o NI 1 A Energy stored in solenoid Usolenoid 2o Bsolenoid 2 Energy density U B2 solenoid A Thur. Nov. 5, 2009 Physics 208, Lecture 19 solenoid 2 o 15 Question A solenoid is stretched to twice its length while keeping the same current and same cross-sectional area. The stored energy Bsolenoid A. Increases oNI B decreases by 2 B. Decreases C. Stays the same 2 U solenoid Bsolenoid A 2 o Energy density decr by 4 Thur. Nov. 5, 2009 Volume increases by 2 Physics 208, Lecture 19 16 Inductor circuit Induced EMF extremely high Breaks down air gap at switch Air gap acts as resistor Thur. Nov. 5, 2009 Physics 208, Lecture 19 17 Question Here is a snapshot of an inductor circuit at a particular time. What is the behavior of the current? A. Increasing B. Decreasing Va I C. Nonzero Constant Vb VL Vb Va L D. Must be zero dI dt R VL IR 0 dI /dt I L Thur. Nov. 5, 2009 E. Need more info Physics 208, Lecture 19 18 Perfect inductors in circuits I Constant current flowing I? - Voltage needed to drive current thru resistor + Thur. Nov. 5, 2009 All Voltage drops = 0 -IR + VL = 0 IR LdI /dt 0 dI /dt I R /L Physics 208, Lecture 19 19 RL circuits - I? dI R I dt L R dI I dt L + Current decreases in time Slow for large inductance Slow for small resistance (inductor fights hard, tries to keep constant current) (little inductor voltage needed to drive current) Time constant L /R Thur. Nov. 5, 2009 Physics 208, Lecture 19 20 RL circuits - I(t) I Ioet /(L / R ) Ioet / + Time constant L /R Thur. Nov. 5, 2009 Physics 208, Lecture 19 21