Changing Magnetic Fields create Electric Fields Physics 102: Lecture 10 Faraday’s Law Changing Magnetic Fields create Electric Fields 1

Last Two Lectures Magnetic fields Forces on moving charges and currents Torques on current loops Magnetic field due to Long straight wire Solenoid

Motional EMF A metal bar slides with velocity v on a track in a uniform B field I V + q Fq Moving + charges in bar experience force down (RHR1) Electrical current driven clockwise! Moving bar acts like a battery (i.e. generates EMF)!! (Recall that e- actually move, opposite current)

Faraday’s Law of Induction: “induced EMF” = rate of change of magnetic flux The principle that unifies electricity and magnetism Key to many things in E&M Generating electricity Microphones, speakers, guitar pickups Amplifiers Computer disks and card readers Demo 371: Helmholz coil and bar magnet

First a preliminary: Magnetic Flux “Counts” number of field lines through loop. B Uniform magnetic field, B, passes through a plane surface of area A. A Magnetic flux F = B A (Units Tm2 = Wb) B A f normal Magnetic flux F  B A cos(f) f is angle between normal and B Note: The flux can be negative (if field lines go thru loop in opposite direction)

Preflight 10.7 Compare the flux through loops a and b. “more lines pass through its surface in that position.” b a FA = B A cos(0) = BA FB = B A cos(90) = 0 Compare the flux through loops a and b. 1) Fa>Fb 2) Fa< Fb

Faraday’s Law of Induction: “induced EMF” = rate of change of magnetic flux Demo 371: Helmholz coil and bar magnet Since F= B A cos(f), 3 things can change F Area of loop Magnetic field B Angle f between normal and B

ACT: Change Area 3 W 2 1 v L v v Which loop has the greatest induced EMF at the instant shown above?

Faraday: Change Area Example F = B A cos(q) W V W vt V L t=0 F0=BLW t Ft=BL(W+vt) F = B A cos(q) EMF Magnitude: What about the sign of the EMF?

Lenz’s Law (EMF direction) V I Bind V Flux is increasing Induced current is clockwise Current loop generates induced B field – from RHR2, into page, opposite external B field! What happens if the velocity is reversed?

Lenz’s Law (EMF direction) V I V Bind Flux is decreasing Induced current is counterclockwise Current loop generates induced B field – from RHR2, out of the page, along external B field! Induced EMF opposes change in flux

Lenz’s Law (EMF Direction) Induced emf opposes change in flux If flux increases: New EMF makes new field opposite to original field If flux decreases: New EMF makes new field in same direction as original field Demo 193: copper pipe and cow magnet. Current induced in pipe opposes movement of magnet. EMF does NOT oppose B field, or flux! EMF opposes the CHANGE in flux

Motional EMF circuit Magnitude of current Direction of Current + q V I = e/R = vBL/R Fq Fbar Direction of Current Clockwise (+ charges go down thru bar, up thru bulb) B field generates force on current-carrying bar Demo: Helmholtz coil and bar magnet Fbar = ILB sin(q), to left (RHR1) Fbar opposes v! Careful! There are two forces: Fbar = force on bar from induced current Fq = force on + charges in bar driving induced current

Motional EMF circuit Magnitude of current Direction of Current What happens if field is reversed? (TRY IT AT HOME) x x x x x x x x x x x x x x x x x Magnitude of current x x x x x x x x x x x x x x x x x V I = e/R = vBL/R x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Direction of Current x x x x x x x x x x x x x x x x x Counter-Clockwise (+ charges go up thru bar, down thru bulb) Direction of force (F=ILB sin(q)) on bar due to magnetic field F always opposes v, bar slows down Must apply external force to keep bar moving Still to left, opposite v

Preflight 10.4 Increase Stay the Same Decrease F=ILB sin(q) To keep the bar moving at the same speed, the force supplied by the hand will have to: Increase Stay the Same Decrease F=ILB sin(q)

Faraday’s Law of Induction: “induced EMF” = rate of change of magnetic flux Demo 371: Helmholz coil and bar magnet Since F= B A cos(f), 3 things can change F Area of loop Magnetic field B Angle f between normal and B 

ACT: Induction cannon (Demo) A solenoid is driven by an increasing current. A loop of wire is placed around it Bsol As current increases in the solenoid, what direction will induced current be in ring? Same as solenoid Opposite of solenoid No current Demo: EM cannon; soleoid S-N N-S loop…they repel each other

Induction cannon (Demo) A solenoid is driven by an increasing current. A loop of wire is placed around it Recall: current loop behaves like bar magnet Opposite currents => opposite polarities Like poles repel! Loop shoots up N S Demo: EM cannon; soleoid S-N N-S loop…they repel each other N S What happens when loop has less resistance? What happens if the loop is broken?

ACT: Change B (Demo) Which way is the magnet moving if it is inducing a current in the loop as shown? Up Down N S Demo: Helmholtz coil and bar magnet Demo: copper pipe and cow magnet Demo 371

ACT: Change B II (cont’d) If I reduce the resistance in the wire, the magnet will fall faster slower at the same speed N S N S

Faraday’s and Lenz’s Law Faraday: Induced emf = rate of change of magnetic flux Lenz: Induced emf opposes change in flux Demo 371: Helmholz coil and bar magnet Since F= B A cos(f), 3 things can change F Area of loop Magnetic field B Angle f between normal and B   Next lecture