From last time… Faraday: Lenz: induced currents oppose change in flux Tue. Nov. 4, 2008 Physics 208, Lecture 19

Faraday’s law EMF no longer zero around closed loop EMF around loop Magnetic flux through surface bounded by path Make comparison to battery. Show that this acts just like battery. Maybe use shaking flashlight to show that this works. EMF no longer zero around closed loop Tue. Nov. 4, 2008 Physics 208, Lecture 19

Lenz’s law Induced current produces a magnetic field. Lenz’s law 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. Do demo with magnet and copper plate. Copper plate in nitrogen. Tue. Nov. 4, 2008 Physics 208, Lecture 19

Question Which way is the magnet moving if it is inducing a current as shown? A. Up B. Down S N Current creates flux up. This must be opposing increase in flux down. So magnet must be falling down N S Tue. Nov. 4, 2008 Physics 208, Lecture 19

Question SN As current is increasing in the solenoid, what direction will current be induced in ring? A. Same as solenoid B. Opposite of solenoid C. No current Tue. Nov. 4, 2008 Physics 208, Lecture 19

What is the direction of the force on the can? Question What is the direction of the current induced in the can? Into page Out of page CW CCW None of the above Can Coil I Ican? End view What is the direction of the force on the can? Tue. Nov. 4, 2008 Physics 208, Lecture 19

A copper guillotine blade falls toward a victim A copper guillotine blade falls toward a victim. It enters field from strong magnets on way down. v What is the direction of the current induced in the loop (blade) as it enters field? CW CCW Depends on field direction What is the direction of the magnetic force on the blade? After questions, do demo. Then ask how induced current and force depends on blade velocity. Then argue that blade reaches terminal velocity. Up Down Depends on field direction. Tue. Nov. 4, 2008 Physics 208, Lecture 19

Eddy current braking Shinkansen Electro- magnets Steel Rail ICE 3 near the Oberhaider Wald Tunnel on the Cologne-Frankfurt high-speed rail line Shinkansen Tue. Nov. 4, 2008 Physics 208, Lecture 19

Eddy current separation side view top view Tue. Nov. 4, 2008 Physics 208, Lecture 19

Back to basics: solenoid flux Uniform field inside Change current -> change flux N turns Wire turns Surface for flux Tue. Nov. 4, 2008 Physics 208, Lecture 19

Magnetic flux in a solenoid N=# of turns, =length of solenoid Flux through one turn =Flux through entire solenoid inductance Tue. Nov. 4, 2008 Physics 208, Lecture 19

Inductance: a general result Flux = (Inductance) X (Current) Change in Flux = (Inductance) X (Change in Current) Faraday’s law: Tue. Nov. 4, 2008 Physics 208, Lecture 19

Changing current in inductor Ideal inductor: Inductance, but zero resistance Constant current: Changing current: Sign of across ideal inductor Opposes change in current. Inductor fights to keep a constant current Tue. Nov. 4, 2008 Physics 208, Lecture 19

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 Total work Energy stored in inductor Tue. Nov. 4, 2008 Physics 208, Lecture 19

Magnetic energy density Energy stored in inductor Solenoid inductance Energy stored in solenoid Bsolenoid Energy density Tue. Nov. 4, 2008 Physics 208, Lecture 19

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 Tue. Nov. 4, 2008 Physics 208, Lecture 19