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

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.

The definition of B

B 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.

BvqF

Magnetic force and field

The definition of B

BvqF

1N/(A.m)C.m/s

N11T

SI unit of B is the Tesla

Gauss101T 4

The sign of q matters!

Magnetic force and field

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)

November in Svalbard (Spitsbergen), 80° North

November near Melbourne (Australia), 37° South

Fine structure of the aurora

field-aligned rays, multiple bands, different heights of the lower border, and dynamics!

photos: Jan Curtis

10

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

11

The lines within are called rays

12

This is called a ‘corona’ or

crown; it is the view looking

straight up the local magnetic

field line (the magnetic zenith)

13

A particularly bright and

beautiful aurora in the

magnetic zenith

14 – it’s fast!

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

1 frame/second color composite

9°, ~17km

Two cameras superimposed, measuring different wavelengths

(colours)

17

Some questions:

what makes the different colours?

how high is it?

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?

19

Auroral Emission Lines

Spectrum of the Sun

Spectrum of the aurora

Energy = h x frequency

Auroral Emission LinesSpectrum of the Sun

Spectrum of the aurora

500 km

100 km

View from the Space Shuttle at 200 km

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.

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

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

24

A movie from the TRACE instrument on the SOHO satellite

Our active Sun

25

From the Sun to the Earth

26

27

Sun-to-aurora TV analogy

Helical pathsSuppose 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 Earth’s field

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.

31

Aurora on other planets

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

Svalbard

33

Svalbard

34

Svalbard Radar

where we do some of our research into the aurora

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

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? A. LeftB. UpC. Into pageD. RightE. DownF. Out 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.

(a) Which particle follows the smaller circleA. pB. e

(b) Does that particle travel A. clockwise or B. anticlockwise?

Answers: (a) electron (smaller mass)

(b) clockwise

pe

Crossed magnetic and electric fieldsNet force:

The forces balance if the speed of the

particle is related to the field strengths by

qvB = qE

BvqEqF

v = E/B (velocity selector)

Measurement of q/m for electronJ J Thomson 1897

EXERCISE: Find an expression for q/m

Sun-to-aurora TV analogy

41

A small part of the sky overhead