Download this only works for your right hand

Magnetic Fields and Currents
The crossover between topics
The force of a magnetic field on an
electric charge
• So, like, yeah, a magnetic field can exert a
force on an electric charge, so long as two
conditions are met:
• The charge has to be moving
• The velocity of the charge has to have a
component perpendicular to the field.
• The force is greatest if the velocity is
completely perpendicular to the field
Which way will the force go?
• To find the direction of the force on a
moving particle, use the right hand rule
• Using your RIGHT HAND, point your four
fingers in the direction of the field
• Point your thumb in the direction of the
velocity of the charge
• Your palm will them face the direction of
the force
• Remember, THIS ONLY WORKS FOR
YOUR RIGHT HAND.
Note on conventions for B-Fields
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B-fields are vectors, just like all the others
So they are represented by arrows
This works fine for left, right, up and down
To represent B-field going into the page,
use X’s (to represent the arrows’ feathers).
• To represent B-field going out of the page,
use circles with dots (to represent the
arrows’ points).
Example Pictures
http://www.analog.com/library/analogdialogue/archives/41-06/AD41-06_FIG-01.jpg
http://session.masteringphysics.com/problemAsset/1003319/16/152258.jpg
Picture of moving charged particle
in B-field
http://www.physics.sjsu.edu/becker/physics51/images/28_13A_Orbit_in_B_field.jpg
Charged particle in E field
• Note the direction of the force on the moving
particle in the E-field.
• If + and – plates were north and south poles of
B-Field, what would the direction of the force
be?
http://knol.google.com/k/-/-/3m2gdefbt6ovt/nd458g/1.jpg
Check for Understanding
• Once more with the volunteers
Magnetic Field
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The symbol for magnetic field is B
Don’t ask me why.
It just is.
Units for magnetic field are Tesla
1 Tesla = 1 Newton/Ampere·meter
Also have defined 1 gauss = 10-4 Tesla
Many magnetic phenomena, like the earth’s
magnetic field, are much smaller than 1 Tesla
• B=
F
or F = Bq0(v sin(θ))
q0(v sin(θ))
Example
• A proton is in an accelerator going 5X106 m/s.
It encounters a magnetic field of 0.4T and is
moving at an angle of 300 with respect to the
field.
• What is the direction and magnitude of the
force on the proton?
• What would these be if it were an electron?
• F = 1.6X10-13 N upward if field is to the right
• Same force downward
Circular Trajectory
• The magnetic force on a charged particle
moving through a B-field will always be
perpendicular to the path
• So it can cause particles to move in circles
• The circle has a radius of r = mv/qB
Bubble chambers
http://www.particlephysics.ac.uk/news/picture-of-the-week/picture-archive/tracks-in-a-hydrogen-bubble-chamber/000329_med.jpg
Check for Understanding
• Once more with the volunteers
Force on a current carrying wire
• If a B-field exerts a force on a moving
charge, it shouldn’t come as a surprise
that it also exerts a force on a current,
since currents are just lots of moving
charges
• F = I L B sin(θ)
• I = current, L = length of wire, B = field
Loudspeakers
http://www.practicalphysics.org/imageLibrary/jpeg500/607.jpg
Torque on a current-carrying wire
• If you can exert a force, you can exert a
torque.
• When a current carrying loop is placed in a
B-field, the loop tends to rotate so that the
perpendicular becomes aligned with the
field
• This is how DC motors work
DC motors
http://cache.eb.com/eb/image?id=63375&rendTypeId=4
Check for Understanding
• Once more with the volunteers
Fields produced by currents
• In addition to magnetic forces on currents,
currents will produce magnetic fields
themselves
• In a long straight wire, the magnetic field
will curl in a circle around the wire
• New RHR: curl your fingers into a half
circle. Point your thumb along the direction
of the current. Your fingers will be curled in
the direction of the field.
A picture will help
• Field created has the
equation:
• B = μ0I/2Πr
• Where μ0 stands for the
permittivity of free
space (don’t ask).
• μ0 = 4 Π X 10-7 T·m/A
http://www.school-for-champions.com/science/images/electromagnetism-magnetic_field.gif
Example
• A wire carries a current of 3 amps. What is
the B-field 0.5 meters perpendicularly
away from the wire?
• B = μ0I/2Πr
• I = 3 amps, r = 0.5 m
Magnetic field of a loop of wire
http://image.tutorvista.com/content/magnetic-effects-electric-current/circular-loop-magnetic-field.jpeg
Solenoid
• A solenoid is a coil of wire that produces a
magnetic field inside. N = # of turns of wire
http://www.siemon.com/uk/white_papers/images/06-05-01-magnets5.gif
Check for Understanding
• Once more with the volunteers