Marathon review of the course: 15 weeks in ~60 minutes! Physics 2102 Gabriela González• 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 energy Gauss’ law!Electric 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 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 currentInduced fields€ E • dA = qenc/ε0S∫€ B • ds =C∫µ0ienc+µ0ε0ddtE • dAS∫=µ0ienc+µ0ε0dΦEdt€ E • dsC∫= −ddtB • dAS∫= −dΦBdtPlus:• V=iR, Q=CV, E=-Ldi/dt • Resistivity: E=Jρ, R=ρL/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=iR Q = CV• Single and multiloop circuits: – Junction rule for current – Loop rule for potential difference • RC/RL circuits: – time constant: τ=RC, L/R – charging/discharging – POTENTIAL across capacitor CANNOT CHANGE SUDDENLY! – CURRENT in inductor CANNOT CHANGE SUDDENLY !Plus: resistors and capacitors in series and in parallel• LC Oscillations: – careful about difference between frequency & angular frequency! – Physical understanding of stages in LC cycle – RLC circuits: energy is dissipated in the resistor.Circuits, circuit elementsWave propagating in x direction: E=Em sin(kx-ωt) j B=Bm sin(kx-ωt) k c=Em/Bm=(µ0ε0)-1/2: speed of light in vacuum S=ExB/µ0=(Em2/µ0c)sin2(kx-ωt) i : Poynting vector I= Em2/2µ0c: intensity, or power per unit area Spherical waves: I=Ps/4πr2 Radiation pressure: F/A=I/c (absorption), F/A=2I/c (reflection) Polarizers: I=I0/2 (unpolarized light), I=I0cos2θ (polarized light)• Refraction: λ = λ0/n, v=c/n, n2sinθ2=n1sinθ1 ⇒ v1sinθ2=v2sinθ1 • Two-beam Interference due to difference in phase : ΔΦ/(2π)=ΔL/λ* ΔL=mλ (constructive), ΔL=(m+1/2)λ (destructive) • Coherent light through a double slit produces fringes: dsin θ=mλ (bright), dsin θ=(m+1/2)λ (dark), fringe spacing Δx=Lλ/dEM waves• 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• 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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