Magnetic Field and moving charges

1 P14-Class 14: OutlineHour 1:Magnetic FieldsExpt. 5: Magnetic FieldsHour 2:Charges moving in B FieldsExam Review2 P14-A New Topic:Magnetic Fields3 P14-Gravitational –Electric FieldsMass mCharge q (±)2ˆmGr=−gr􀁇2ˆeqkr=Er􀁇Create:Eq=FE􀁇􀁇gm=Fg􀁇􀁇Feel:Also saw…Dipole p=×τpE􀁇􀁇􀁇Create:Feel:4 P14-Magnetism –Bar MagnetLike poles repel, opposite poles attract5 P14-Demonstration:Magnetic Field Linesfrom Bar Magnet6 P14-Demonstration:Compass (bar magnet) in Magnetic Field Linesfrom Bar Magnet7 P14-Magnetic Field of Bar Magnet(1) A magnet has two poles, North (N) and South (S)(2) Magnetic field lines leave from N, end at S8 P14-Bar Magnets Are Dipoles!•Create Dipole Field•Rotate to orient with FieldIs there magnetic “mass” or magnetic “charge?”NO! Magnetic monopoles do not exist in isolation9 P14-Bar Magnets Are Dipoles!•Create Dipole Field•Rotate to orient with FieldIs there magnetic “mass” or magnetic “charge?”NO! Magnetic monopoles do not exist in isolation10 P14-Magnetic Monopoles?Magnetic Dipoleq-qp􀁇Electric Dipoleµ􀁇When cut: 2 monopoles (charges)When cut: 2 dipolesMagnetic monopoles do not exist in isolationAnother Maxwell’s Equation! (2 of 4)0Sinqdε⋅=∫∫EA􀁇􀁇􀁷S0d⋅=∫∫BA􀁇􀁇􀁷Gauss’s LawMagnetic Gauss’s Law11 P14-Fields: Grav., Electric, MagneticMass mCharge q (±)2ˆmGr=−gr􀁇2ˆeqkr=Er􀁇No Magnetic Monopoles!Create:Eq=FE􀁇􀁇gm=Fg􀁇􀁇Feel:Also saw…Dipole pDipole µ=×τpE􀁇􀁇􀁇Create:Feel:=×τµB􀁇􀁇􀁇→E􀁇←B􀁇12 P14-What else is magnetic?13 P14-Magnetic Field of the EarthAlso a magnetic dipole!North magnetic pole located in southern hemisphere14 P14-Earth’s Field at MITWe will measure these components15 P14-Experiment 5:Bar Magnet & Earth’s Magnetic Field 16 P14-Visualization: Bar Magnet & Earth’s Magnetic Field (http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/27-barmagontable/27-barmag320.html)17 P14-Magnetic Field B Thus Far…Bar Magnets (Magnetic Dipoles)…•Create:Dipole Field•Feel: Orient with FieldDoes anything else create or feel a magnetic field?18 P14-Demonstration:TV in Field19 P14-Moving Charges Feel Magnetic ForceBq=×FvB􀁇􀁇􀁇Magnetic force perpendicular both to:Velocity vof charge and magnetic field B20 P14-Magnetic Field B: UnitsBq=×FvB􀁇􀁇􀁇Since ()()mAN1smCN1ndmeter/secocoulombnewton UnitsB⋅=⋅==This is called 1 Tesla (T)41 T = 10 Gauss (G)21 P14-Recall:Cross Product22 P14-Notation DemonstrationXXXXXXXXXXXXXXXXOUT of page“Arrow Head”INTO page“Arrow Tail”23 P14-Cross Product: MagnitudeComputing magnitude of cross product A x B:sinθ=CAB􀁇􀁇􀁇x=CAB􀁇􀁇􀁇|C|:􀁇area of parallelogram24 P14-Cross Product: DirectionRight Hand Rule #1:x=CAB􀁇􀁇􀁇1) Curl fingers of right hand in the direction that moves A(green vector) to B (redvector)through the smallest angle 2) Thumb of right hand will point in direction of the cross product C(orange vector)http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/vectorfields/14-CrossProduct/14-crossprod320.html25 P14-Cross Product: Signsjkijikijkikjkijkjiˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆ−=×=×−=×=×−=×=×Cross Product is Cyclic (left column)Reversing A& Bchanges sign (right column)26 P14-PRS Questions:Right Hand Rule27 P14-Putting it Together: Lorentz Force()q=+×FEvB􀁇􀁇􀁇􀁇This is the final word on the force on a chargeBq=×FvB􀁇􀁇􀁇Eq=FE􀁇􀁇Electric FieldsCharges Feel…Magnetic Fields28 P14-Application: Velocity SelectorWhat happens here?29 P14-Velocity SelectorParticle moves in a straight line when ()0netq=+×=FEvB􀁇􀁇􀁇􀁇 EvB⇒=30 P14-PRS Question:Hall Effect31 P14-Exam Review