Chapters 27 and 25 (excluding 25.4)MagnetismGeomagnetism: It’s a life saver!Origin of GeomagnetismBroken SymmetryA magnetic field does not diverge, its’ field line circulateMagnetic Fields exerts a force on charged particlesDirection of ForceUnitsMagnetic FluxMotion of Charged Particles in a Magnetic FieldMathematicallyCombined Force: Lorentz ForceVelocity selectorLeaving ElectrostaticsSlide 16Can’t we all get along? (Blame Benjamin Franklin)Current DensityAt the speed of what?Charge carrier densityResistivity and Ohm’s LawResistanceRelationship between Resistance and ResistivityOhm’s LawPower in resistorsBand Theory of SolidsForce Law from current perspectiveForce and Torque on a Current LoopDiagramForcesDirectionsTorquesSides of length, a, have a net torqueMagnetic Moment, mMagnets on an atomic levelHall Effect1Chapters 27 and 25 (excluding 25.4)2Magnetism Magnetism known to the ancientsMost Famous Magnet: EarthNorth=South! (today)Seems to have flipped several timesBased on orientation of magnetic layers in the earth Is Moving!From 1580 to 1820, compass changed by 35o||Bearth|| = 8 x 1022 J/TSN3Geomagnetism: It’s a life saver!Sun and other galactic radiation sources emit charged particlesMagnetic fields divert charged particlesAstronauts can get large radiation dosesGeomagnetic anomaly off of Tierra del Fuego4Origin of GeomagnetismUranium and other radioactive materials provide heat through alpha decayThis heat keeps the earth’s core (mostly iron) hotThe molten iron circulates5Broken SymmetryThere are no magnetic monopoles i.e the simplest magnetic system is a north pole-south pole system Simplest Electric SystemSimplest Magnetic System6A magnetic field does not diverge, its’ field line circulate 00 AdBBqAdEEallyMathematicoenclosedoenclosedGauss’s Law for Magnetic Fields7Magnetic Fields exerts a force on charged particlesForce is proportional to the charge,q, the velocity of the charge,v, and the strength of the magnetic field,BSince v, B, F are vectorsWe need a way to multiply a vector by a vector and get a vector: cross-productF=qv x B||F||=qvB sin where  is the angle between v and B8Direction of Force9UnitsUnits of B = newtons/(coulomb* meter/second)Called Tesla (T)Coulomb/second called Ampere (A)T=N/(A*m)cgs units are gauss (G) where 1 T = 104 GEarth’s magnetic field at any point is about 1 GLargest magnetic field is 45 T (explosion-induce about 120 T)10Magnetic Flux AdBBMagnet flux through a closed surface=0This is the field lines through a surface Units=weber (Wb) and 1 Wb=1 T*m11Motion of Charged Particles in a Magnetic FieldSince F is perpendicular to v, there is no acceleration but it does change the directionA particle moving initially perpendicular to B remains perpendicular to BParticle’s path is a circle traced out with a constant speed, v0WsovFthenBvqFIfdtrdvandrdFWortxvandxFW12MathematicallyqBmvRqvBrvmqvBFrvmF22mqBfmqBffqBmTqBmvrbutvrT22122R is the radius of the charged particles path is the angular frequency of the particlef is called the cyclotron frequency13Combined Force: Lorentz ForceIf there is a static electric field, E, and a static magnetic field, B, a force is exerted on the particle equivalent to BvqEqF14Velocity selectorLet E and B be perpendicular as shown below. We will solve for the velocity of particles are in equilibrium (F=0).BEvqvBqEqvBqEFBvqEqF015Leaving ElectrostaticsElectrostatics meant charges did not moveWe will consider “steady” currents Steady currents are constant currentsCurrent: a stream of moving chargestdtidqqdtdqi016UnitsAmpere (A) = Coulomb/second (C/s)1 A in two parallel straight conductors placed one meter apart produce a force of 2x10-7 N/m on each conductor17Can’t we all get along? (Blame Benjamin Franklin)For physicists:The current arrow is drawn in the direction in which the positive charge carriers would movePositive carriers move from positive to negativeFor engineers:The current arrow is drawn in the direction in which the negative charge carriers would moveNegative carriers move from negative to positiveA negative of a negative is a positive so at the end of the day, we should all agree. (Technically speaking, the engineers have it right.)18Current DensityAd AdJiAqqqqAdIf the current is uniform and parallel to dA then i=JA or J=i/A19At the speed of what?When a conductor has no current, the electrons drift randomly with no net velocityWhen a conductor has a current, the electrons still drift randomly but they tend to drift with a velocity, vd in a direction opposite of the electric fieldDrift speed is TINY (about 10-5 to 10-4 m/s) compared to the random velocity of 106 m/sSo if the electrons only move at 0.1mm/s then why do the lights come on so fast?20Charge carrier densityLet n=number of charge carriers/volumeIf wire has cross-sectional area, A, and length, L, then volume = ALTotal number of charges, q=n(AL)eLet t be the time that the charges traverse the wire with drift velocity, vd, this must be t=L/vddddvneJAiJifnAevvLeALntqi)(Charge carrier current density21Resistivity and Ohm’s LawEach material has a property called resistivity, , which is defined as=E/J where E is the electric field and J is the charge density (actual definition of Ohm’s law)Units: (V/m)/(A/m2)=*mThe reciprocal of resistivity is conductivity, .J=EMaterials are “ohmic” when  is constantIf materials do not depend on this simple relation, then the material is non-ohmic22Resistance“resistance” to current flow How much voltage required to make current flowUnits: ohm =V/A ()SymboliVR 23Relationship between Resistance and ResistivityALRorLARLAiVAiLVJEthenAiJLVEthenLdanddVEif24Ohm’s LawA current through a device is always proportional to the potential difference appliedViresistorVidiodeBoth obey V=iR but the resistor obeys Ohm’s law while the diode does not25Power in