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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