lec20_022307_-_Magnetics

lec20_022307_-_Magnetics - Exam II: Thursday, March...

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Unformatted text preview: Exam II: Thursday, March Magnetics 1st Big Picture Electrostatics Circuits I= - Qo - e = I oe RC t t Review recitations next week (NO QUIZ) Practice Exam on LON-CAPA posted now LON- RC Circuit Discharge: Time Constant : = RC Q = Qo e - tf Magnetics Charge: Q = Qf 1- e - t I= R e - t = I oe - t Chapter 27: Magnetic Force on Charges and Currents Chapter 28: Sources of Magnetic Field Chapter 29: Electromagnetic Induction Chapter 30: Self Inductance and Inductors Optics 1 Friday, 23 February 2007 2 Friday, 23 February 2007 Magnetic Force Empirically, it is determined that: Fmag = qv B B is the magnetic field experienced by the charge q and has SI units of Tesla (T). Cross Product Review C = A B = -B A Magnitude: 1T = 1 N/C N s N = = m/s m C A m 10-4 tesla q=0 v=0 F =0 F =0 C = AB sin is the angle between A and B 1 Gauss = vB F =0 0.5 G: Magnetic field of Earth 50 T: Maximum DC magnetic field strength 65 T: Maximum pulse field strength F v&B C is perpendicular to both A and B Direction of C is found using the Right Hand Rule! ^ i C = A B = Ax Bx Friday, 23 February 2007 Calculate rigorously: Read more at http://www.magnet.fsu.edu http://www.magnet.fsu.edu Friday, 23 February 2007 3 ^ j Ay By ^ k (Ay Bz - Az B y ) i^ - j Az = ( Ax Bz - Az Bx ) ^ + ^ Bz (Ax B y - Ay Bx ) k 4 1 Question Given the situation at the instant shown below, the acceleration of the electron is: Motion of a Charge in an Uniform Magnetic Field y B F = qv B vx, y x RHR ^ F in - k vx , y +q v B F =0 ^ F in -k v = constant ^ a in -k 2 v r A. B. C. D. E. To the right Up Down Into the page Out of the page v z y F = qv B F = qv B 2 v r Circular motion : Fc = mac = m z v qv B = m qrB = mv = p (momentum!) a Circular motion : = v r qrB = mr = = 2f Friday, 23 February 2007 5 Friday, 23 February 2007 f = qB 2m qB m Cyclotron Frequency! 6 Question A point charge of (+q) enters a region of uniform (+q B-field as shown. What is its trajectory? A. Circle in the x-y plane B. Circle in the y-z plane C. Helix traveling in the xxdirection D. Helix traveling in the yydirection E. Helix traveling in the zzdirection y Question A point charge of (+q) enters a region of uniform (+q B-field as shown. What is its kinetic energy as compared to before entering the B-field? BA. Bigger B. x y B B v q z Smaller v q z x C. The same Friday, 23 February 2007 7 Friday, 23 February 2007 8 2 Magnetic Force on a I-carrying Wire Fmag = qv B Magnetic Force on a Curved I-carrying Wire F = qv B y I d B d dF y dq x F = nqA vd B Q = nqA dF dF = (dq )v B d = dq B dt dq = d B dt dF = Id B v= d dt dF = Id B B d = I B R v = vd I = nqvd A Friday, 23 February 2007 x dF = Id B d R F= d = Rd - sin i^ + cos ^ j 9 Friday, 23 February 2007 ( ) )( ^ = - IRBd (cos i + sin ^ ) j ^ j dF = - IRB (cos i + sin ^ ) d ^ = - IRB[sin i - cos ^ ] j = - IRB[(0) i^ - (- 1 - 1) ^ ] j ( 0 ^ ^ = IRd - sin i + cos ^ - B k j ) 0 = -2 IRB ^ j 10 3 ...
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