Lecture 17Chapter 29Magnetic FieldsMagnetic Fields (1)• Analogous to electric field, a magnet produces a magnetic field, B• Set up a B field 2 ways:• Moving electrically charged particles – Current in a wire• Intrinsic magnetic field – Basic characteristic of elementary particles such as an electronMagnetic Fields (2)• When charged particle moves through Bfield, a force acts on the particle• Magnitude of FBis• where φis the angle between v and B• SI unit for B is tesla, TBvqFBrrr×=φsinvBqFB=rmANsmCNT⋅=⋅= 111Magnetic Fields (3)• FB= 0 if – Charge, q = 0– Particle is stationary– v and B are parallel (φ=0) or anti-parallel (φ=180)• FBis maximum if– v and B are ⊥⊥⊥⊥ to each otherφsinqvBBvqFB=×=rrrMagnetic Fields (4)BvqFBrrr×=• FBacting on charged particle is always ⊥⊥⊥⊥ to v and B• FBnever has component || to v• FBcannot change v or K.E. of particle • FBcan only change direction of vMagnetic Fields (5)•Right-hand rule –For positive charges the thumb of right hand points in direction of FBwhen the fingers sweepv into B through the smaller angle φ• For negative charges FBpoints in opposite directionMagnetic Fields (6)• Checkpoint #1 - What is the direction of FBon the particle with the v and B shown?• Use right-hand rule - don’t forget charge A) +zB) -xC) zeroBvqFBrrr×=Magnetic Fields (7)• Check yourself using matrix notation• Write vectors for v and B()()()kabbajabbaiabbabbbaaakjibayxyxzxzxzyzyzyxzyxˆˆˆˆˆˆ−+−−−==×rrMagnetic Fields (8)• Magnetic field lines• Direction of tangent to field line gives direction of B at that point• Denser the lines the stronger the B fieldMagnetic Fields (9)• Magnetic field lines enter one end (south) of magnet and exit the other end (north)• Opposite magnetic poles attract, like magnetic poles repelMagnetic Fields (10)• What happens if there is both an E field and a B field?• Both fields produce a force on a charged particle• If the two fields are ⊥⊥⊥⊥ to each other call them crossed fieldsMagnetic Fields (11)• Cathode ray tube – used in television• Can deflect a beam of electrons by – E field from charged parallel-plates– B field from magnet • Adjust E and B fields to move electron beam across fluorescent screenMagnetic Fields (12)• Checkpoint #2 – E field out of page, Bfield to left• A) Rank 1,2, and 3 by magnitude of net Fon particle, greatest first• What direction is FEat 1?Out of page• Is it the same for all directions of v ?YESMagnetic Fields (13)•A) Rank magnitude of net F for 1, 2 and 3.2, then 1 & 3 tie• B) Which direction could have net F of zero?Direction 4• What is direction of FB for 1,2,3 and 4?1) FB= 02) FBout of page3) FB= 04) FBinto pageMagnetic Fields (14)• Electrons moving in a wire (= current) can be deflected by a B field called the Hall effect• Creates a Hall potential difference, V, across the wire • Can measure the wire’s charge density when at equilibrium FE= FBMagnetic Fields (15)• Electrons have drift velocity, vdin direction opposite the current, i• B field into page causes force, FBto right• Electrons pile up on right hand side of strip• Leaves + charges on left and produce an E field inside the strip pointing to rightMagnetic Fields (16)• E field on electron produces a FEto the left• Quickly have equilibrium where FE= FB• E field gives a V across the strip• Left side is at a higher potentialEdV =Magnetic Fields (17)• Can measure the number of charge carriers per unit volume, n, at equilibrium BEFF =qEFE=)90sin(BeveEd=BvqFBrr×=BvEd=Magnetic Fields (18)• Remember from Chpt. 27 that drift speed is neAineJvd==neAiBBvEd==EeAiBn =Magnetic Fields (19)• Replacing E by EdV =VeAiBdEeAiBn ==Magnetic Fields (20)• If l is the thickness of the strip• Finally getVleiBn =dAl =Magnetic Fields (21)• Checkpoint #3 – Have 6 choices for velocity, v of rectangle in ± x, ±y, and ±z• A) Rank 6 choices by V across solid, greatest first• First figure out direction of FBfor each v•For ±x, FBis zero (φ=0,180)•For ±y, FBis into (out of) page across distance d•For ±z, FBis moving up (down) page across 2dBvqFBrr×=Magnetic Fields (22)• A) Rank 6 choices by V across solid, greatest first• FE= FBbut opposite direction •So • Found ±z to be across 2d, ±y across d and ±x to be zero ±z, ±y, ±xvBE=EdV =vBdV =vFEFBMagnetic Fields (23)• B) For which direction is the front face at lower V ?•Get V across front face if v is in y direction • To get lower V at front face FEmust point from back to front so want FBinto
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