Electricity and magnetismElectric currents and magnetic fieldsSlide 3Moving charges and magnetic field and magnetic forceThe force between two wires with currentsThe definition of the current unit Ampere and examplesexampleBiot-Savart lawExamplemagnetic field of a long straight wireSlide 11Ampere’s LawExamples of using Ampere’s LawSlide 14Slide 15Slide 16Slide 171Electricity and magnetismElectricity Electric charge, electric field and potential, current, resistance and capacitanceMagnetismMoving electric charge, magnetic field, magnetic force on moving chargesElectric charge generates electric field:Gauss’ LawElectric field exert forces on a charge inside it: F = qEElectric potential and voltage: E = -grad.U, Voltage = ΔU = Electric field energy density: Capacitor stores electric energy:Electric current generates magnetic field:Ampere’s Law: The magnetic field lines are always loops around the electric currents.Magnetic field exerts forces on moving charges: Lorentz force: F = qv×BOn a section of a wire: F = IL×Btorque on a loop of a wire: τ = IA×B = μ ×BMagnetic dipole: μ = IAThe Hall effect: ΔV = BI/(nqw)Electric field moves charges and moving charges form current: Resistance and resistivity: ,Circuits, power, battery emf, connection rules (R and C in series and parallel) and Kirchhoff’s rules.0/QdESEBAdrE2021EEu221CVPE dtdqtI )(ALR2021EEuId0lB2Electric currents and magnetic fieldsMagnets were discovered in ancient times. The Chinese discovered the Earth magnet and invented the compass 220 BC.2000+ yearsEarth's magnetic field (and the surface magnetic field) is approximately a magnetic dipole, with one pole near the north pole (see Magnetic North Pole) and the other near the geographic south pole (see Magnetic South Pole). An imaginary line joining the magnetic poles would be inclined by approximately 11.3° from the planet's axis of rotation. The cause of the field is explained by dynamo theory. SouthNorth3Electric currents and magnetic fieldsIn 1820, Hans Christian Oersted discovered that currents generate magnetic fields: Direction: Right-hand ruleR Magnitude:4Moving charges and magnetic field and magnetic forceCurrent comes from moving charges. Magnetic field actually relates to moving charge as electric field relates to charge, through the force F on the charge:Electric field E and charge q: F = qE, here the force F is the electric charge q.Magnetic field B and moving charge qv: F = qv×B, here the force F is the electric charge q which is moving with velocity v.(comes from the cross product of two vectors)Combine the two formulas, one has the famous Lorentz force law:F = qE + q v×B5The force between two wires with currentsThe B field generated by I1 in wire 1 at the location of wire 2 isFor small charge dq in wire 2, the force it experiences follows Lorentz law: dF = dq v×BCheck the vectors directions, the magnitude dF is dF = dq vBdq v = dqdl/dt = dq/dt dl = I2dlRIB210BBdqRLIIdlRIIRIdlIBvdqFLLL222210021010020So F over L isThe direction of the force F depends on the direction of the two currents: same direction, attract; difference direction: repel.6The definition of the current unit Ampere and examplesWhen I1 = I2 = I, and the same direction, then the current I is defined to be 1 Ampere if the two wires are 1 meter apart, and the force between them is 2×10-7 N per 1 meter wire length.In the diagram, one current flows through the straight wire and another current flows around the wire loop, with the magnitudes shown. What are the magnitude and direction of the force exerted on the wire loop by the current in the straight wire?7example8Biot-Savart lawWhen the current follows a wire that is not straight, we use Biot-Savart law to calculate the B field this current generates at a point P in space:This is similar to Coulomb’s Law that relates electric field to electric charges:The B field generated by the full section of wire is then: The formular relates magnet field to currents.304 rIddrBl304 rdIrBlldBdrrE304 rdqdrE3041rdqand9ExampleUsing Biot-Savart Law to derive the formula for magnetic field of a long straight wire:10magnetic field of a long straight wire11Examplemagnetic field at the center of a half circle:12Ampere’s LawAmpere’s Law: enclosedSCIdSd00 jlB13Examples of using Ampere’s LawCurrent genersted magnetic fieldOutside a long straight wireInside the wireOf a sheet conductorOf a solenoidOf a toroid14Examples of using Ampere’s LawCurrent genersted magnetic fieldInside the wire15Examples of using Ampere’s LawCurrent genersted magnetic fieldof a sheet conductor16Examples of using Ampere’s LawCurrent genersted magnetic fieldOf a solenoid17Examples of using Ampere’s LawCurrent genersted magnetic fieldOf a
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