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Physics 2102 Gabriela González Physics 2102 Marathon review of the course: 15 weeks in ~60 minutes! Overview • 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 Electric Field • 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 Gauss’ law! – 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 Electric fields Magnetic 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 (BiotSavart’s law, Ampere’s law) • Magnetic dipoles: field produced by a dipole, torque on a dipole Magnetic fields Induced fields • Changing magnetic flux creates an induced electric field (and a current if there is a wire!): Faraday’s law d B C E dl dt • Changing electric flux creates an induced magnetic field: Ampere-Maxwell’s law, displacement current d E B dl 0 0 dt C Induced fields Maxwell’s equations E dA q enc / 0 S d B ds 0ienc 0 0 dt C C d E ds dt Plus: S B dA 0 S dE E dA 0ienc 0 0 dt dB B dA dt S F q( E v B) 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=iR Q = CV di E L dt DC 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 circuits Plus: resistors and capacitors in series and in parallel AC 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. 1 LC Circuits, circuit elements Electromagnetic waves Wave propagating in x direction: E=Em sin(kx-t) j B=Bm sin(kx-t) k c=Em/Bm=(00)-1/2: speed of light in vacuum S=ExB/0=(Em2/0c)sin2(kx-t) i : Poynting vector I= Em2/20c: intensity, or power per unit area Spherical waves: I=Ps/4pr2 Radiation 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 : D/(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/d EM waves Overview • 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 Summary • 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 summer!