Magnetic FieldsChapter 26 26.2 The force exerted by a magnetic field Definition of B 26.3 Motion of a charged particle in a magnetic field ApplicationsA circulating charged particle Crossed fields: discovery of the electron The cyclotron and mass spectrometer
The magnetic fieldMagnetic 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.
The definition of BB is defined in terms of the magnetic force FB 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
The definition of BSI unit of B is the TeslaThe sign of q matters!Magnetic force and field
CHECKPOINT: An electron moves perpendicular to a magnetic field. What is the direction of B? LeftUpInto pageRightDownOut of pageAnswer: C. For an electron the force is in the direction of (v x B)
November in Svalbard (Spitsbergen), 80 North
November near Melbourne (Australia), 37 South
Fine structure of the aurorafield-aligned rays, multiple bands, different heights of the lower border, and dynamics!photos: Jan Curtis
*Aurora takes many shapes and forms; these are called arcs and stretch from one horizon to another
*The lines within are called rays
*This is called a corona or crown; it is the view looking straight up the local magnetic field line (the magnetic zenith)
*A particularly bright and beautiful aurora in the magnetic zenith
* its fast!
This view is about half the sky, using a white light camera, at 3 speed
1 frame/second color composite9, ~17km Two cameras superimposed, measuring different wavelengths (colours)
what makes the different colours?
how high is it?
*Fast incoming particles strike oxygen and nitrogen gases high in the atmosphere, causing them to make light of different colours.What is the aurora?
*Auroral Emission LinesSpectrum of the SunSpectrum of the auroraEnergy = h x frequency
Auroral Emission LinesSpectrum of the SunSpectrum of the aurora
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.
A circulating charged particle
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
*A movie from the TRACE instrument on the SOHO satelliteOur active Sun
*From the Sun to the Earth
*Sun-to-aurora TV analogy
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.
Helical paths in a magnetic bottle and in the Earths field
A string of auroral substorms following a Coronal Mass Ejection (CME) impact on Earth Observed by the University of Iowas VIS Imager on the Polar SatelliteAuroral 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.
*Aurora on other planets
2 hours of data from IMAGE satellite, measuring Lyman Alpha emissions in ultraviolet from precipitating protonsSvalbard
*Svalbard Radar where we do some of our research into the aurora
*First results from new camera ASK (Auroral Structure and Kinetics)ASK1: 20 seconds of data at 32 fps18:21:10 18:21:30 UT22 October 20063 degree field of view in magnetic zenith
Electric fields acting along the magnetic field
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 FB on the particle? LeftUpInto pageRightDownOut of page
Answers: (a) +z (out)(b) x (left, negative particle)(c) 0
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.
Which particle follows the smaller circleA. pB.e
Does that particle travel clockwise or anticlockwise?Answers: (a) electron (smaller mass)(b) clockwise
Crossed magnetic and electric fieldsNet force:The forces balance if the speed of the particle is related to the field strengths by qvB = qE v = E/B (velocity selector)
Measurement of q/m for electronJ J Thomson 1897
Sun-to-aurora TV analogy
*A small part of the sky overhead
*This slide is really to demonstrate a few of the features that matter when it comes to research about aurora. The pictures on the left demonstrate the importance of the magnetic field in the rayed structures. They also show the changes in the height of the lower borders along the length of these arcs. But these changes are not staticthe dynamics is the crucial feature. The multiple bands are also part of the story.there are many scale sizes in aurora, and what I mostly concentrate on is the very smallest of these.*This is not a bad simulation of a large burst of solar particles or Coronal Mass Ejection, hitting the earths magnetosphere and interacting with the magnetic fields through a process called reconnection, which in turn accelerates the particles into the polar regions. Here the aurora seems to be caused by little rods of light but it serves the purpose well.*This movie is from our first night of very dynamic aurora. There are many GB of data to chose from so this is just a random chunk made into a video.