Physics 272
February 20
Spring 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html
Prof. Philip von Doetinchem
philipvd@hawaii.edu
Phys272 - Spring 14 - von Doetinchem - 341
Where we stand
Electric charges are
sources of electric fields
0 (constant time,
conservative electric force)
Phys272 - Spring 14 - von Doetinchem - 342
Magnetism
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Examples: permanent
magnets, compass in
earth magnetic field
Magnetic forces arise
from moving electric
charges
Electric charges react to
magnetic field
Source: http://de.wikipedia.org/wiki/Magnet
First: focus on how electric charges react to magnetic
fields
Permanent magnets:
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Exert forces on each other
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Exert forces on unmagnetized objects containing iron
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Magnetism
http://www.youtube.com/watch?v=jq8WOUFeCcg
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Magnetic poles vs. electric charge
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Initially: magnets described in terms of poles
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North: bar shaped magnetic material (free to rotate) points North
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South: bar shaped magnetic material (free to rotate) points South
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North and South attract each other
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North-North and South-South repels each other
Objects containing iron are attracted by South and North
poles
Earth is a magnet:
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geographic poles
close to magnetic
poles: not totally
parallel
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Magnetic axis moves
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Magnetic poles vs. electric charge
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Important: no isolated magnetic North and
South poles exist
Major difference to positive and negative
electric charges
Ørsted found that a compass needle
was deflected by a current carrying
wire
Magnetic forces are due to
interactions of moving electrons in atoms
Magnetized objects have
coordinate motion of certain
atomic electrons
Hans Christian Ørsted
1777-1851
Source: http://de.wikipedia.org/wiki/Hans_Christian_%C3%98rsted
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Unmagnetized objects do not
have coordinated motion
Electric and magnetic interactions are
connected and bring us back to slide 1
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Magnetic field
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A moving charge or a current creates a magnetic
field in the surrounding space (in addition to electric
field)
The magnetic field exerts a force on any other
moving charge or current that is present in the field.
For now: don't worry about how exactly magnetic
field is created.
Magnetic field is a vector field: a vector associated
with each point in space.
Direction towards the north pole of a compass
needle.
Phys272 - Spring 14 - von Doetinchem - 347
Magnetic forces on moving charges
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Magnitude of the force is proportional to amount of
charge
Magnitude of the force is proportional to the
magnetic field strength.
Magnitude of the force is proportional to the velocity
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electric force is always the same: no matter if charge
moves or not!
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Particle at rest does not feel magnetic force
Force is perpendicular to the velocity and magnetic
field
Phys272 - Spring 14 - von Doetinchem - 348
Magnetic forces on moving charges
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Charges of same amount, but opposite sign
→ feel force of same magnitude, but opposite
direction
Magnitude of force
(use component of magnetic field perpendicular to
velocity)
Phys272 - Spring 14 - von Doetinchem - 349
Magnetic forces on moving charges
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Magnetic field of the earth: 0.1mT
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Magnetic field in atoms: 10T
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Largest magnetic field in lab: 45T
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Pulse magnetic fields produce up to: 120T
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Magnetic field and electric field:
Phys272 - Spring 14 - von Doetinchem - 350
The World's Strongest Magnet
http://www.youtube.com/watch?v=6wH1kq7gfuU
Phys272 - Spring 14 - von Doetinchem - 351
Measuring magnetic fields with test charges
http://www.youtube.com/watch?v=YbzBTdU7iRU
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Measure deflection of moving charges in the presence of a magnetic field
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Example:
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old televisions contained an electron beam in a cathode-ray tube
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Velocity is known
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If beam and magnetic field (anti)parallel → no force → no deflection
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If beam and magnetic perpendicular → maximum deflection
Phys272 - Spring 14 - von Doetinchem - 352
Proton in a magnetic field
Force in negative y direction:
Phys272 - Spring 14 - von Doetinchem - 353
Magnetic field lines and magnetic flux
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Magnetic field lines work
in a similar way as for the
electric field
Tangents on field lines
represent direction of
magnetic field
Higher density of lines
represents a higher
magnetic field
Be careful: magnetic force is not in the direction of
magnetic lines, is perpendicular to B and velocity
Magnetic field lines never intersect
Phys272 - Spring 14 - von Doetinchem - 358
Magnetic flux and Gauß's law for magnetism
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Magnetic flux ΦB describes
the number of field lines
poking through an area A
Every surface can be
separated in little surface
elements dA
Magnetic flux
is a scalar quantity
Wilhelm Weber
1804-1891
Source: http://de.wikipedia.org/wiki/Wilhelm_Eduard_Weber
Phys272 - Spring 14 - von Doetinchem - 359
Magnetic flux and Gauß's law for magnetism
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Electric flux through a closed surface is proportional
to total enclosed charge
No equivalent to electric charge exist in
magnetism!
No magnetic monopoles = total magnetic flux
through a closed surface is always zero.
Gauß's law for magnetism:
no magnetic monopoles: no ending field lines
→ magnetic field lines have to be loops
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Magnetic flux calculation
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Motion of charged particles in a magnetic field
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Charge particle in magnetic field follows Newton's law
Example: uniform
magnetic field into the
plane
Velocity and magnetic
field are perpendicular
Charged particle is kept
on a circle
Magnetic forces point
all towards the center
Force is always perpendicular to velocity
→ cannot change the magnitude of the velocity
→ can only change direction
Magnetic force can never do work on charged particle in any
type of magnetic field → velocity stays constant.
Phys272 - Spring 14 - von Doetinchem - 363
Motion of charged particles in a magnetic field
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Centripetal acceleration equals magnetic force:
If the velocity is not perpendicular to magnetic field
→ particle moves on a helix
Phys272 - Spring 14 - von Doetinchem - 364
Magnetic bottle
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Magnetic force points
away from denser region
Angle between drift velocity
and field lines changes can
cause the particle to
reverse direction
Radiation belts around
the Earth trap charged
particles
Near the poles radiation
belt particles can interact
with atmosphere and can
cause colorful light emissions
Source: http://de.wikipedia.org/wiki/Van-Allen-G%C3%BCrtel
Phys272 - Spring 14 - von Doetinchem - 365
Aurora borealis
http://www.youtube.com/watch?v=aIVzZMeMQxA
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Helical particle motion in a magnetic field
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Helical particle motion in a magnetic field
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Velocity selector
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Mass spectrometers
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Use to measure masses of ions
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Use velocity filter
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Leave filter and continue in region with magnetic field only
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Ions are deflected in a circle
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Higher masses have a larger radius
Phys272 - Spring 14 - von Doetinchem - 370