2. Magnetism1 Review on Magnetism Chapter 28

3. Magnetism2 Refrigerators are attracted to magnets!

4. Magnetism3 Where is Magnetism Used?? Motors Navigation – Compass Magnetic Tapes –Music, Data Television –Beam deflection Coil Magnetic Resonance Imaging (MRI) High Energy Physics Research

5. Magnetism4 Cathode Anode (28 – 8)

6. Magnetism5 Consider a Permanent Magnet NS The magnetic Field B goes from North to South.

7. Magnetism6 Units

8. Magnetism7 Typical Representation

9. Magnetism8 A Look at the Physics q There is NO force on a charge placed into a magnetic field if the charge is NOT moving. q If the charge is moving, there is a force on the charge, perpendicular to both v and B. F = q v x B There is no force if the charge moves parallel to the field.

10. Magnetism9 The Lorentz Force This can be summarized as: v F B q m or:  is the angle between B and V

11. Magnetism10 Nicer Picture

12. Magnetism11 The Wire in More Detail B out of plane of the paper Assume all electrons are moving with the same velocity v d. L

13. Magnetism12. i (28 – 12)

14. Magnetism13 Current Loop Loop will tend to rotate due to the torque the field applies to the loop. What is force on the ends??

15. Magnetism14 C C Top view Side view (28 – 13)

16. Magnetism15 Dipole Moment Definition Define the magnetic dipole moment of the coil  as:  =NiA  =  x B We can convert this to a vector with A as defined as being normal to the area as in the previous slide.

17. Magnetism16 (28 – 14)

18. Magnetism17 LL L R R R (28 – 15)

19. Magnetism18 Motion of a charged particle in a magnetic Field

20. Magnetism19 Trajectory of Charged Particles in a Magnetic Field ++++++++++++++++++++++++++++++++++++++++ v B F ++++++++++++++++++++++++++++++++++++++++ v B F (B field points into plane of paper.)

21. Magnetism20 Trajectory of Charged Particles in a Magnetic Field ++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++ v v BB F F (B field points into plane of paper.) Magnetic Force is a centripetal force

22. Magnetism21 Review of Rotational Motion  atat arar a t = r  tangential acceleration a r = v 2 / r radial acceleration The radial acceleration changes the direction of motion, while the tangential acceleration changes the speed. r  s  = s / r  s =  r  ds/dt = d  /dt r  v =  r  = angle,  = angular speed,  = angular acceleration Uniform Circular Motion  = constant  v and a r constant but direction changes a r = v 2 /r =  2 r F = ma r = mv 2 /r = m  2 r KE = ½ mv 2 = ½ mw 2 r 2 v  arar

23. Magnetism22

24. Magnetism23 ++++++++++++++++++++++++++++++++++++++++ Radius of a Charged Particle Orbit in a Magnetic Field v B F r Centripetal Magnetic Force Force =

25. Magnetism24 Cyclotron Frequency ++++++++++++++++++++++++++++++++++++++++ v B F r The time taken to complete one orbit is:

26. Magnetism25 Mass Spectrometer Smaller Mass

27. Magnetism26

28. Magnetism27 An Example A beam of electrons whose kinetic energy is K emerges from a thin-foil “window” at the end of an accelerator tube. There is a metal plate a distance d from this window and perpendicular to the direction of the emerging beam. Show that we can prevent the beam from hitting the plate if we apply a uniform magnetic field B such that

29. Magnetism28 Problem Continued r

30. Magnetism29 #14 Chapter 28 A metal strip 6.50 cm long, 0.850 cm wide, and 0.760 mm thick moves with constant velocity through a uniform magnetic field B= 1.20mTdirected perpendicular to the strip, as shown in the Figure. A potential difference of 3.90 ηV is measured between points x and y across the strip. Calculate the speed v. FIGURE 28- 37 Problem 14.

31. Magnetism30 21. (a) Find the frequency of revolution of an electron with an energy of 100 eV in a uniform magnetic field of magnitude 35.0 µT. (b) Calculate the radius of the path of this electron if its velocity is perpendicular to the magnetic field.

32. Magnetism31 39. A 13.0 g wire of length L = 62.0 cm is suspended by a pair of flexible leads in a uniform magnetic field of magnitude 0.440 T. What are the (a) magnitude and (b) direction (left or right) of the current required to remove the tension in the supporting leads?