Lecture 17 Chapter 29 Magnetic Fields Magnetic 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 electron Magnetic Fields 2 When charged particle moves through B field a force acts on the particle r r r FB qv B Magnitude of FB is r FB q vB sin where is the angle between v and B SI unit for B is tesla T N N 1T 1 1 C m s A m Magnetic Fields 3 r r r FB qv B qvB sin FB 0 if Charge q 0 Particle is stationary v and B are parallel 0 or anti parallel 180 FB is maximum if v and B are to each other Magnetic Fields 4 r r r FB qv B FB acting on charged particle is always to v and B FB never has component to v FB cannot change v or K E of particle FB can only change direction of v Magnetic Fields 5 Right hand rule For positive charges the thumb of right hand points in direction of FB when the fingers sweep v into B through the smaller angle For negative charges FB points in opposite direction Magnetic Fields 6 Checkpoint 1 What is the direction of FB on the particle with the v and B shown Use right hand rule don t forget charge A z B x B C zero r r r F qv B Magnetic Fields 7 Check yourself using matrix notation Write vectors for v and B i j k r r a b ax a y az a ybz by az i axbz bxaz j axby bxa y k bx by bz Magnetic 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 field Magnetic Fields 9 Magnetic field lines enter one end south of magnet and exit the other end north Opposite magnetic poles attract like magnetic poles repel Magnetic 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 fields Magnetic 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 screen Magnetic Fields 12 Checkpoint 2 E field out of page B field to left A Rank 1 2 and 3 by magnitude of net F on particle greatest first What direction is FE at 1 Out of page Is it the same for all directions of v YES Magnetic Fields 13 What is direction of FB for 1 2 3 and 4 1 FB 0 2 FB out of page 3 FB 0 4 FB into page 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 Magnetic 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 FB Magnetic Fields 15 Electrons have drift velocity vd in direction opposite the current i B field into page causes force FB to right Electrons pile up on right hand side of strip Leaves charges on left and produce an E field inside the strip pointing to right Magnetic Fields 16 E field on electron produces a FE to the left Quickly have equilibrium where FE FB E field gives a V across the strip V Ed Left side is at a higher potential Magnetic Fields 17 Can measure the number of charge carriers per unit volume n at equilibrium FE FB FE qE r r FB qv B eE evd B sin 90 E vd B Magnetic Fields 18 Remember from Chpt 27 that drift speed is J i vd ne neA iB E vd B neA iB n EeA Magnetic Fields 19 Replacing E by V Ed iB iBd n EeA VeA Magnetic Fields 20 If l is the thickness of the strip A l d Finally get iB n Vle 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 FB for each v r r FB qv B For x FB is zero 0 180 For y FB is into out of page across distance d For z FB is moving up down page across 2d Magnetic Fields 22 A Rank 6 choices by V across solid greatest first FE FB but opposite direction E vB V Ed So V vBd Found z to be across 2d y across d and x to be zero z y x FE v FB Magnetic Fields 23 B For which direction is the front face at lower V v FE Get V across front face if v is in y direction To get lower V at front face FE must point from back to front so want FB into page y
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