February 24, 2014 Physics for Scientists & Engineers 2, Chapter 27 1

Magnetism

February 24, 2014 Physics for Scientists & Engineers 2, Chapter 27 2

Magnetism !  The Sun has massive magnetic fields as do other stars !  The Earth also has a magnetic field !  In the region of Magnesia, ancient Greeks found naturally

occurring minerals (lodestone) that attracted and repelled each other and attracted various material such as iron

!  The minerals are various forms of iron oxide and are called permanent magnets

!  Examples: refrigerator magnets and magnetic door latches !  They are all made of compounds of iron, nickel, or cobalt !  If you touch an iron needle to a piece of magnetic lodestone, the

iron needle will be magnetized !  If you then float this iron needle in water, the needle will point

toward the north pole of the Earth (approximately!) !  We call the end of the magnet that points north the

north magnetic pole of the magnet and the other end the south magnetic pole of the magnet

February 24, 2014 Physics for Scientists & Engineers 2, Chapter 27 3

Permanent Magnets - Poles

!  Magnets exert forces on one another

!  If we bring together two permanent magnets such that the two north poles are together or two south poles are together, the magnets will repel each other

!  If we bring together a north pole and a south pole, the magnets will attract each other

February 24, 2014 Physics for Scientists & Engineers 2, Chapter 27 5

Broken Permanent Magnet !  If we break a permanent magnet

in half, we do not get a separate north pole and south pole

!  When we break a bar magnet in half, we always get two new magnets, each with its own north and south pole

!  Unlike electric charge that exists as positive (proton) and negative (electron) separately, there are no separate magnetic monopoles (an isolated north pole or an isolated south pole)

!  Scientists have carried out extensive searches for magnetic monopoles; all results are negative

!  Magnetism is not caused by magnetic particles! Magnetism is caused by electric currents

February 24, 2014 Physics for Scientists & Engineers 2, Chapter 27 6

Magnetic Field Lines !  Permanent magnets interact with each other at a distance,

without touching !  In analogy with the electric field, we define a magnetic field

to describe the magnetic force !  As we did for the electric field, we represent the magnetic field using magnetic field lines

!  As with electric field lines, closer spacing of magnetic field lines indicates a higher field strength

!  The field is tangent to the field lines !  The direction of the field can be measured at any point by

moving a compass needle around in a magnetic field and noting the direction that a compass needle points

B

Magnetic Field Lines – Bar Magnet

February 24, 2014 Physics for Scientists & Engineers 2, Chapter 27 7

Magnetic Field Lines

February 24, 2014 Physics for Scientists & Engineers 2, Chapter 27 8

February 24, 2014 Physics for Scientists & Engineers 2, Chapter 27 9

The Earth’s Magnetic Field !  The Earth itself is a magnet !  It has a magnetic field sort of like a bar magnet (but not

exactly like a bar magnet) !  The poles of the Earth’s magnetic field are not aligned with

the Earth’s geographic poles defined as the endpoints of the axis of the Earth’s rotation

!  The Earth’s magnetic field is not a simple dipole field because it is distorted by the solar wind •  Protons from the Sun moving at 400 km/s

!  The Earth’s magnetic field is important because it protects the Earth from these cosmic rays

!  Cosmic rays are diverted to the poles and sometimes captured in the Van Allen radiation belts

The Earth’s Magnetic Field

February 24, 2014 Physics for Scientists & Engineers 2, Chapter 27 10

S

N

Solar Wind

Superposition of Magnetic Fields !  If several sources of magnetic field are present, the magnetic field at any point in space is given by the superposition of the magnetic fields from all sources

!  This superposition of fields follows from the principle of superposition of forces

!  The superposition principle can be stated mathematically as

!  … just as for electric fields

February 24, 2014 Physics for Scientists & Engineers 2, Chapter 27 11

Btotal

r( ) =B1r( )+B2r( )+ ...+

Bnr( )

Magnetic Force !  The magnetic force exerted by a magnetic field on a moving

charged particle is given by

!  The direction of the magnetic force is perpendicular to both the velocity of moving positively charged particle and the magnetic field and is given by the right hand rule

!  The force is in the opposite direction for a negatively charged particle

February 24, 2014 Physics for Scientists & Engineers 2, Chapter 27 12

FB = qv ×

B

February 24, 2014 Physics for Scientists & Engineers 2, Chapter 27 13

Magnetic Force

!  The magnitude of the the magnetic force on a moving charged particle is

where θ is the angle between the velocity of the charged particle and the magnetic field

!  No magnetic force acts on a charged particle moving parallel or anti-parallel to the magnetic field

!  The maximum magnetic force occurs when the charged particle is moving perpendicular to the magnetic field

FB = q vBsinθ

FB = q vB

Magnetic Force and Work !  The magnetic force is perpendicular to the velocity of a

moving charged particle

!  The magnetic force can change the direction of the velocity of the moving charged particle but not its magnitude

!  The kinetic energy remains the same !  The magnetic force does no work on the moving charged

particle !  On the other hand, the electric field can easily be used to do

work on a particle

February 24, 2014 Physics for Scientists & Engineers 2, Chapter 27 14

Fiv = 0 and ai

v = 0

February 24, 2014 Physics for Scientists & Engineers 2, Chapter 27 18

Units of Magnetic Field Strength !  The magnetic field strength has received its own named

unit, the tesla (T), named in honor of the physicist and inventor Nikola Tesla (1856-1943)

!  A tesla is a rather large amount of magnetic field strength !  Sometimes you will find magnetic field strength state in

units of gauss (G), (not an official SI unit)

1 T = 1 Ns

Cm=1 N

Am

1 G = 10-4 T10 kG = 1 T

February 24, 2014 Physics for Scientists&Engineers 2 19

Example: Proton in B Field !  A uniform magnetic field with magnitude

B=1.2mT is directed upward (green dots are the tips of the B-field vectors) in a chamber. A proton with kinetic energy E=8.48 10-13J enters the chamber and is moving horizontally from south to north. What magnetic deflecting force acts on the proton (m=1.67 10-27 kg)?

!  Idea: Use F=qvBsinΘ. First, figure out the velocity v.

February 24, 2014 Physics for Scientists&Engineers 2 20

Example: Proton in B Field !  A uniform magnetic field with magnitude

B=1.2mT is directed upward (green dots are the tips of the B-field vectors) in a chamber. A proton with kinetic energy E=8.48 10-13J enters the chamber and is moving horizontally from south to north. What magnetic deflecting force acts on the proton (m=1.67 10-27 kg)?

!  Angle between B-field direction and velocity of the proton: Θ=90°

!  Direction of F: Use Right Hand Rule !  Small force but large acceleration for light particle

February 24, 2014 Physics for Scientists & Engineers, Chapter 22 21

Cathode Ray Tube

PROBLEM !  Consider a cathode ray tube !  In this tube, a potential difference of ΔV = 111 V accelerates

electrons horizontally in an electron gun !  Positively charged anodes focus the electrons into a beam !  Horizontal and vertical deflecting plates use potential

differences to steer the beam !  In the main part of the cathode ray tube, there is a magnetic field with magnitude B = 3.40·10-4 T