2. Magnetic Fields Chapter 26 26.2 The force exerted by a magnetic field Definition of B 26.3 Motion of a charged particle in a magnetic field Applications A circulating charged particle Crossed fields: discovery of the electron The cyclotron and mass spectrometer

3. The magnetic field Magnetic field lines of the earth depicted by iron filings around a uniformly magnetized sphere. Magnetic field lines exit from the north magnetic pole. For the earth this is the geographic south pole. William Gilbert discovered that the earth is a natural magnet in 1600.

4. The definition of B B is defined in terms of the magnetic force F B exerted on a moving electrically charged particle. Experimentally it is observed that, when a charge q has velocity v in a magnetic field, there is a force on the charge that is  proportional to q and to v,  greatest when charge moves perpendicular to field, and zero when parallel to the field – in general it is proportional to the sine of the angle between v and B.  perpendicular to both the velocity and the field. Magnetic force and field

5. The definition of B SI unit of B is the Tesla The sign of q matters! Magnetic force and field

6. CHECKPOINT: An electron moves perpendicular to a magnetic field. What is the direction of B? A.Left B.Up C.Into page D.Right E.Down F.Out of page Answer: C. For an electron the force is in the direction of – (v x B)

7. November in Svalbard (Spitsbergen), 80° North

8. November near Melbourne (Australia), 37° South

10. Fine structure of the aurora field-aligned rays, multiple bands, different heights of the lower border, and dynamics! photos: Jan Curtis

11. 10 Aurora takes many shapes and forms; these are called ‘arcs’ and stretch from one horizon to another

12. 11 The lines within are called rays

13. 12 This is called a ‘corona’ or crown; it is the view looking straight up the local magnetic field line (the magnetic zenith)

14. 13 A particularly bright and beautiful aurora in the magnetic zenith

15. 14 – it’s fast!

16. This view is about half the sky, using a white light camera, at  3 speed

17. 1 frame/second color composite 9°, ~17km Two cameras superimposed, measuring different wavelengths (colours)

18. 17 Some questions: what makes the different colours? how high is it?

19. 18 Fast incoming particles strike oxygen and nitrogen gases high in the atmosphere, causing them to make light of different colours. What is the aurora?

20. 19 Auroral Emission Lines Spectrum of the Sun Spectrum of the aurora Energy = h x frequency

21. Auroral Emission Lines Spectrum of the Sun Spectrum of the aurora 500 km 100 km View from the Space Shuttle at 200 km

22. 26.3 Motion of a point charge in a magnetic field The magnetic force is always perpendicular to the velocity of the particle. The magnetic force thus changes the direction of the velocity but not its magnitude. Therefore magnetic fields do no work on particles and do not change their kinetic energy.

23. The circular path of electrons moving in the magnetic field (into page) produced by two large coils. Charged particle moving in a plane perpendicular to a uniform magnetic field (into page). A circulating charged particle

24. False colour photo showing tracks of a 1.6 MeV proton (red) and a 7 MeV alpha particle (yellow) in a cloud chamber. Radius of curvature is proportional to the momentum, and inversely proportional to the charge. A circulating charged particle

25. 24 A movie from the TRACE instrument on the SOHO satellite Our active Sun

26. 25 From the Sun to the Earth

27. 26

28. 27 Sun-to-aurora TV analogy

29. Helical paths Suppose that a charged particle enters a uniform magnetic field with a velocity that is not perpendicular to B. There is no force component, and thus no acceleration component parallel to B, so the component of the velocity parallel to B remains constant. The path of the particle is a helix. Cloud chamber photo of helical path of an electron in a magnetic field.

30. Helical paths in a ‘magnetic bottle’ – and in the Earth’s field

31. A string of auroral “substorms” following a Coronal Mass Ejection (CME) impact on Earth Observed by the University of Iowa’s VIS Imager on the Polar Satellite Auroral emissions seen from space: the light occurs in two ring shaped regions around each magnetic pole. Charged particles are guided there by the magnetic field.

32. 31 Aurora on other planets

33. 2 hours of data from IMAGE satellite, measuring Lyman Alpha emissions in ultraviolet from precipitating protons Svalbard

34. 33 Svalbard

35. 34 Svalbard Radar where we do some of our research into the aurora

36. 35 First results from new camera ASK (Auroral Structure and Kinetics) ASK1: 20 seconds of data at 32 fps 18:21:10 – 18:21:30 UT 22 October 2006 3 degree field of view in magnetic zenith Electric fields acting along the magnetic field

37. CHECKPOINT : Here are three situations in which a charged particle with velocity v travels through a uniform magnetic field B. In each situation, what is the direction of the magnetic force F B on the particle? A.Left B.Up C.Into page D.Right E.Down F.Out of page Answers: (a) +z (out) (b) –x (left, negative particle) (c) 0

38. CHECKPOINT : The figure shows the circular paths of two particles that travel at the same speed in a uniform B, here directed into the page. One particle is a proton; the other is an electron. (a)Which particle follows the smaller circle A. p B.e (b)Does that particle travel A.clockwise or B.anticlockwise? Answers: (a) electron (smaller mass) (b) clockwise p e

39. Crossed magnetic and electric fields Net force: The forces balance if the speed of the particle is related to the field strengths by qvB = qE v = E/B (velocity selector)

40. Measurement of q/m for electron J J Thomson 1897 EXERCISE: Find an expression for q/m

41. Sun-to-aurora TV analogy

42. 41 A small part of the sky overhead