Slide 1OverviewElectric FieldElectric fieldsMagnetic FieldsMagnetic fieldsInduced fieldsInduced fieldsMaxwell’s equationsResistors, Capacitors, InductorsDC CircuitsDC circuitsAC CircuitsCircuits, circuit elementsElectromagnetic wavesWave OpticsEM wavesOverviewSummaryPhysics 2102 Marathon review of the course:15 weeks in ~60 minutes!Physics 2102Gabriela GonzálezOverview•Fields: electric & magnetic–electric and magnetic forces on electric charges–potential energy, electric potential, work (for electric fields), electric and magnetic energy densities–fundamental laws on how fields are produced: Maxwell’s equations! •Circuits & components:–Capacitors, resistors, inductors, batteries–Circuits: circuits with R and batteries, RC, LR, LC. •Waves :– Speed, frequency, wavelength, polarization, intensity– Wave optics: interference•Forces due to electric fields: F=qE, Coulomb’s Law•Electric field due to:–single point charge, several point charges –Electric dipoles: field produced by a dipole, electric torque on a dipole –charged lines: straight lines, arcs–surface charges: conducting and insulating planes, disks, surfaces of conductors–volume charges: insulating spheres, conductors (E=0 inside). •Electric flux, Gauss’ law, applied to spherical, cylindrical, plane symmetry •Electric potential of a single charge, of several charges, of distributed charges.•Work, potential energyElectric FieldGauss’ law!Electric fieldsMagnetic Fields•Force exerted by a magnetic field on a charge, on a current.•Magnetic field lines: always closed!•Magnetic fields created by currents:wires, loops, solenoids (Biot-Savart’s law, Ampere’s law)•Magnetic dipoles: field produced by a dipole, torque on a dipoleMagnetic fieldsInduced fields•Changing magnetic flux creates an induced electric field (and a current if there is a wire!): Faraday’s law•Changing electric flux creates an induced magnetic field: Ampere-Maxwell’s law, displacement currentdtdldEBC-CEdtdldB00Induced fieldsMaxwell’s equations€ E • dA = qenc/ε0S∫-SdAB 0€ B • ds =C∫μ0ienc+ μ0ε0ddtE • dAS∫= μ0ienc+ μ0ε0dΦEdt€ E • dsC∫= −ddtB • dAS∫= −dΦBdt)( BvEqFPlus:Resistors, Capacitors, Inductors•V=iR, Q=CV, E=-Ldi/dt•Resistivity: E=Jr, R=rL/A•Parallel plate, spherical, cylindrical capacitors•Capacitors with dielectrics•Resistors, capacitors in series and in parallel •Power delivered by a battery: P=iE•Energy dissipated by a resistor: P=i2 R=V2/R•Energy stored in capacitors, inductors (energy stored in electric, magnetic fields)•Ideal and real batteries (internal resistance)V=iRQ = CVdtdiLEDC Circuits•Single and multiloop circuits: –Junction rule for current–Loop rule for potential difference•RC/RL circuits: –time constant: t=RC, L/R–charging/discharging–POTENTIAL across capacitor CANNOT CHANGE SUDDENLY!–CURRENT in inductor CANNOT CHANGE SUDDENLY !DC circuitsPlus: resistors and capacitors in series and in parallelAC Circuits•LC Oscillations: –careful about difference between frequency & angular frequency!–Physical understanding of stages in LC cycle–RLC circuits: energy is dissipated in the resistor.LC1Circuits, circuit elementsElectromagnetic wavesWave propagating in x direction:E=Em sin(kx-wt) jB=Bm sin(kx-wt) kc=Em/Bm=(m0e0)-1/2: speed of light in vacuumS=ExB/m0=(Em2/m0c)sin2(kx-wt) i : Poynting vectorI= Em2/2m0c: intensity, or power per unit areaSpherical waves: I=Ps/4pr2Radiation pressure: F/A=I/c (absorption), F/A=2I/c (reflection)Polarizers: I=I0/2 (unpolarized light), I=I0cos2q (polarized light)Wave Optics• Refraction: l = l0/n, v=c/n, n2sinq2=n1sinq1 v1sinq2=v2sinq1 • Two-beam Interference due to difference in phase : DF/(2p)=DL/l DL=ml (constructive), DL=(m+1/2)l (destructive) • Coherent light through a double slit produces fringes: dsin q=ml (bright), dsin q=(m+1/2)l (dark), fringe spacing Dx=Ll/dEM wavesOverview•Fields: electric & magnetic–electric and magnetic forces on electric charges–potential energy, electric potential, work (for electric fields), electric and magnetic energy densities–fundamental laws on how fields are produced: Maxwell’s equations! •Circuits & components:–Capacitors, resistors, inductors, batteries–Circuits: circuits with R and batteries, RC, LR, LC. •Waves :– Speed, frequency, wavelength, polarization, intensity– Wave optics: interferenceSummary•Think about and understand basic concepts! •Look at your past exams and quizzes: why didn’t you get 100%? Predict your problems in the final exam!•Study the equation sheet, invent a problem for each formula. •Read all lecture slides, review hwk problems and problems in class.•Practice with a couple of past exams: timing is important!•Save time to eat lunch and relax the hour before the exam.•Enjoy the
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