Homework due next Tuesday 11:59 PM Next Sunday: no in-person office hour (try a skype office hour 7:45 8:15?)

Transcription

1 Homework due next Tuesday 11:59 PM Next Sunday: no in-person office hour (try a skype office hour 7:45 8:15?) SUNDAY Nov 18: SECOND HOUR EXAM 6:10-7:30 PM in SEC 111 (Ch ) -- no recitations the previous Friday and following Monday COME DOWN AND PLAY WITH THE EDDY CURRENT DEMOS BEFORE CLASS

2 New law that shows how CHANGES in magnetic field create this new kind of electric field FARADAY S LAW! E d s! = d! B d A! C S dt Iine integral surface integral (magnetic flux) Loop C is the boundary of the surface S

3 Computing flux when magnetic field is not uniform or surface is not flat

4 B(r), surface S Magnetic flux through a surface B1 A 1 n ^ B2 A 2 n ^ Flat surface, B uniform on each part: Φ = ( B 1 ˆn)A 1 + ( B 2 ˆn)A 2

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6 Not flat Divide into two or more flat pieces Do a surface integral Use the fact that magnetic field lines are closed loops

7 Simplest way to change the flux: Change the magnetic field, keeping the loop fixed Example: pass a bar magnet through the loop

8 OTHER WAYS TO CHANGE THE MAGNETIC FLUX THROUGH A LOOP Move the loop into or out of a region with B field Rotate the loop in a uniform field: angle between B and n changes, so Φ changes Change the size of the loop in a uniform field Examples: pull the loop closed a moving metal rod on U-shaped wire

9 Move the loop into or out of a region with B field

10 With the normal vector out of the page, the flux is negative and increasing (becoming less negative). The induced current flows clockwise to produce a negative flux, opposing this change

11 OTHER WAYS TO CHANGE THE MAGNETIC FLUX THROUGH A LOOP Move the loop into or out of a region with B field Rotate the loop in a uniform field: angle between B and n changes, so Φ changes Change the size of the loop in a uniform field Examples: pull the loop closed a moving metal rod on U-shaped wire

12 Change the shape of the loop

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14 If you have a wire loop, there is induced currrent Induced current feels a force from the magnetic field

15 Move the loop into or out of a region with B field Φ Negative increasing (less negative) Induced current is clockwise Magnetic force on induced current in loop opposite to direction of motion

16 If you have a wire loop, there is induced currrent Induced current feels a force from the magnetic field Magnetic force opposes the motion Slows down (magnetic force does negative work) Or keeps moving with applied force that does work Mechanical work done on the system equals the energy dissipated in the resistive wire

17 Eddy currents The moving bar magnet may feel a force from the magnetic field produced by the induced current Galvanometer demo Falling magnet in copper tube (copper tube = stack of wire loops) New demo: magnet rolling down a copper ramp force opposes the motion The induced current may feel a force from the magnetic field LOTS OF DEMOS

18 EDDY CURRENTS AND FORCES Piece of metal moves in B field Currents induced are called eddy currents Force on induced currents opposite to the direction of motion Lower resistivity means larger currents, larger forces DEMOS Swinging plates ROLLING DISKS

19 CHANGING MAGNETIC FIELD INDUCES CURRENT AND EXERTS FORCE Levitating ring demo Sinusoidally varying current in ring makes a changing field Induces current in sheet that creates a time-averaged net upward force on the ring

20 CHANGING MAGNETIC FIELD INDUCES CURRENT AND EXERTS FORCE Ring flinger demo Sinusoidally varying current in solenoid makes a changing magnetic field The changing field along the axis induces current in ring The changing radial field creates a time-averaged net upward force on the ring How to make this force smaller? How to make this force bigger?

21 C! E d! s = d dt S! B d! A Current in wire loop is induced by electric field created by the changing magnetic flux Electric field is created whether a wire loop is there or not

22 C! E d! s = d dt S! B d! A If B(t) = a t, what is E(r)? E(r) 2πr = - d/dt (a t π r 2 ) = -a π r 2 E(r) = -a r / 2 (negative means pointing clockwise)

23 CHANGING MAGNETIC FIELD INDUCES CURRENT AND EXERTS FORCE Can crusher demo Surge of current through the coil when capacitor is discharged Changing magnetic field induces current around the can

24 EXAMPLE: UNIFORM B FIELD with changing magnitude inside solenoid INDUCED E FIELD C IF THERE IS A WIRE LOOP on the curve C, current will flow MAGNETIC FORCE ON THE WIRE LOOP CURRENT PULSE: I, B increase from zero CAN CRUSHER DEMO

25 CAN CRUSHER DEMO CURRENT PULSE: I, B increase from zero (RLC with switch closed at t=0) Magnetic force on loop is INWARD