Changing Magnetic Fields create Electric Fields Physics 102: Lecture 10 Faraday’s Law Changing Magnetic Fields create Electric Fields Exam 1 tonight Be sure to bring your ID and go to correct room All you need is a #2 pencil and calculator No cell phones No I-pods, laptops, etc. 1

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

Today: Faraday’s Law The principle that unifies electricity and magnetism Key to many things in E&M Generating electricity Microphones, speakers and tape decks Amplifiers Computer disks and card readers 7

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 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) 22

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 73% 27% 24

“induced emf” = rate of change of magnetic flux Faraday’s Law of Induction: This is new physics and not simply an application of stuff you already know “induced emf” = rate of change of magnetic flux Since F= B A cos(f), 3 things can change F Area of loop Magnetic field B Angle f between A and B Demo 371: Helmholz coil and bar magnet 26

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 28 demo: 1093

ACT: Change Area 3 W 2 1 v L v v Which loop has the greatest induced EMF at the instant shown above? 1 moves right - gets 4 more field lines. 2 moves down - gets 0 more field lines. 3 moves down - only gets 2 more lines. 1 is gaining flux fastest! E1 = BvL E 2 = 0 E 3 = BvW 35

Example: Change Area F = B A cos(q) W V W vt V L I t=0 F0=BLW t Ft=BL(W+vt) F = B A cos(q) EMF Magnitude: EMF Direction: B is out of page and F is increasing so EMF creates B field (inside loop) going into page. 38

Motional EMF circuit Magnitude of current Direction of Current Moving bar acts like battery e = vBL B - + Magnitude of current V I = e/R = vBL/R Direction of Current Clockwise (+ charges go down thru bar, up thru bulb) Demo: Helmholtz coil and bar magnet Direction of force (F=ILB sin(q)) on bar due to magnetic field What changes if B points into page? To left, slows down DEMO: 371 15

Motional EMF circuit Magnitude of current Direction of Current Moving bar acts like battery e = vBL B 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 x x x x x x x x x x x x x x x x x I = e/R = vBL/R 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 Still to left, slows down 18

Preflight 10.4 Increase Stay the Same Decrease F=ILB sin(q) Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure. To keep the bar moving at the same speed, the force supplied by the hand will have to: 28% 61% 10% Increase Stay the Same Decrease F=ILB sin(q) B and v still perpendicular (q=90), so F=ILB just like before! 19

Preflight 10.5 Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure. To keep the bar moving to the right, the hand will have to supply a force in the opposite direction. 53% 47% True False Current flows in the opposite direction, so force from the B field remains the same! 20

ACT: Change B SN As current is increasing in the solenoid, what direction will current be induced in ring? Same as solenoid Opposite of solenoid No current Demo: EM cannon; soleoid S-N N-S loop…they repel each other  Solenoid current (counter-clockwise)  B-field (upwards) =>  Flux thru loop EMF will create opposite B-field (downwards) Induced loop current must be clockwise Demo 157 40

ACT: Change B II Which way is the magnet moving if it is inducing a current in the loop as shown? Up Down S N N S Demo: Helmholtz coil and bar magnet Demo: copper pipe and cow magnet Field from magnet is down. Induced current creates field up - opposite original. So flux from magnet must be increasing. Magnet must be falling down Demo 371 42

Change f A flat coil of wire has A=0.2 m2 and R=10W. At time t=0, it is oriented so the normal makes an angle f0=0 w.r.t. a constant B field of 0.12 T. The loop is rotated to an angle of =30o in 0.5 seconds. Calculate the induced EMF. Example Fi = B A cos(0) Ff = B A cos(30) n B A f Demo with big orange magnet and flip coil Demo with Helmholtz coil and bar magnet…change angle e = 6.43x10-3 Volts What direction is the current induced? B upwards and F decreasing. Induced B will be in same direction (opposes change). Current must be counter clockwise. Demo 68, 371 44

Magnetic Flux Examples A conducting loop is inside a solenoid (B=monI). What happens to the flux through the loop when you… Increase area of solenoid? Nothing Increase area of loop? Increases Increase current in solenoid? Increases F  B A cos(f) Rotate loop slightly? Decreases 48

Magnetic Flux II Example A solenoid (B=monI) is inside a conducting loop. What happens to the flux through the loop when you… Increase area of solenoid Increases Increase area of loop Nothing Increase current in solenoid Increases F  B A cos(f) 50

Demo: Change B As current is increasing in the solenoid, what direction will current be induced in ring? Demo: EM cannon; soleoid S-N N-S loop…they repel each other  Solenoid current (counter-clockwise)  B-field (upwards) =>  Flux thru loop EMF will create opposite B-field (downwards) Induced loop current must be clockwise Demo 157 40

Good Luck Tonight! 50

Motional EMF, Preflight 10.1 B Moving + charge feels force downwards: F = q v B sin(q) v Velocity + F B Moving + charge still feels force downwards: + - L v - + Potential Difference = F L/q EMF = q v B sin(q) L/q = v B L skip Velocity Only 22% got this correct on the preflight!! 10

Preflight 10.2 Which bar has the larger motional emf? v a b v E = v B L sin(q) q is angle between v and B skip Case a: q = 0, so E = 0 Case b: q = 90, so E = v B L 62% got this correct. 12