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

• 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

• 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