Thur. Nov. 5, 2009Physics 208, Lecture 191 From last time… Faraday: Motional EMF Moving conductor generates electric potential difference to cancel motional EMF Changing flux generates EMF

Motional EMF Charges in metal feel magnetic force Tue. Nov. 2, 2009Physics 208, Lecture 182 Charges move, build up at ends of metal Equilibrium: electric force cancels magnetic force

Tue. Nov. 2, 2009Physics 208, Lecture 183 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)

B(t) Coil in magnetic field Uniform B-field increasing in time Flux in z-direction increasing in time Thur. Nov. 5, 2009Physics 208, Lecture 194 Lenz’ law: Induced EMF would produce current to oppose change in flux Induced current

B(t) 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 difference from one end to other Opposes Faraday EMF ΔV = - EMF Thur. Nov. 5, 2009Physics 208, Lecture 195 Increasing with time Compare motional EMF

Thur. Nov. 5, 2009Physics 208, Lecture 196 Coil can generate it’s own flux Uniform field inside solenoid Change current -> change flux N turns Wire turns Surface for flux

Thur. Nov. 5, 2009Physics 208, Lecture 197 ‘Self’-flux in a solenoid Flux through one turn  =Flux through entire solenoid N=# of turns, =length of solenoid inductance

Thur. Nov. 5, 2009Physics 208, Lecture 198 Inductance: a general result Flux = (Inductance) X (Current) Change in Flux = (Inductance) X (Change in Current)

Thur. Nov. 5, 2009Physics 208, Lecture 199 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, 2009Physics 208, Lecture 1910 Question A solenoid is stretched to twice its length while keeping the same current and same cross-sectional area. The inductance A.Increases B.Decreases C.Stays the same Field, hence flux, have decreased for same current

Fixed current through ideal inductor For fixed resistor value Current through inductor I = V batt /R Flux through inductor = LI Constant current -> Flux through inductor doesn’t change No induced EMF Voltage across inductor = 0 Thur. Nov. 5, 2009Physics 208, Lecture 1911 V batt R L I Ideal inductor: coil has zero resistance

V batt R L I VbVb VaVa Try to change current You increase R in time: Current through inductor starts 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 Thur. Nov. 5, 2009Physics 208, Lecture 1912 time R(t)R(t)

Thur. Nov. 5, 2009Physics 208, Lecture 1913 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 V a >V B

Thur. Nov. 5, 2009Physics 208, Lecture 1914 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

Thur. Nov. 5, 2009Physics 208, Lecture 1915 Magnetic energy density Energy stored in inductor Solenoid inductance Energy stored in solenoid B solenoid Energy density

Thur. Nov. 5, 2009Physics 208, Lecture 1916 Question A solenoid is stretched to twice its length while keeping the same current and same cross-sectional area. The stored energy A.Increases B.Decreases C.Stays the same B decreases by 2 Energy density decr by 4 Volume increases by 2

Thur. Nov. 5, 2009Physics 208, Lecture 1917 Inductor circuit Induced EMF extremely high Breaks down air gap at switch Air gap acts as resistor

Question Here is a snapshot of an inductor circuit at a particular time. What is the behavior of the current? Thur. Nov. 5, 2009Physics 208, Lecture 1918 I VbVb VaVa A.Increasing B.Decreasing C.Nonzero Constant D.Must be zero E.Need more info

Thur. Nov. 5, 2009Physics 208, Lecture 1919 Perfect inductors in circuits Constant current flowing All Voltage drops = 0 I I? Voltage needed to drive current thru resistor -IR +  V L = 0 + -

Thur. Nov. 5, 2009Physics 208, Lecture 1920 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) I? + - Time constant

Thur. Nov. 5, 2009Physics 208, Lecture 1921 RL circuits I(t) + - Time constant