Physics 2102 Gabriela Gonz lez 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 volume charges insulating spheres conductors E 0 inside Gauss law 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 E dl dt C 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 S 0 d B ds 0ienc 0 0 dt C C d E ds dt Plus S S B dA 0 S d E E dA 0ienc 0 0 dt d B B dA dt 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 wt j B Bm sin kx wt k c Em Bm m0e0 1 2 speed of light in vacuum S ExB m0 Em2 m0c sin2 kx wt i Poynting vector I Em2 2m0c 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 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 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
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