Explain what are Lienard-Wiechert Potentials. In what situation we need to use the Lienard-Wiechert potentials (V and A)?
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- Charying an oljeci by indluction requires no direct conlact with the oljeci Inducing the chargr. a True: or b) False?The main mathematical tools of electromagnetism are (so far): Gauss, Stokes, Helmholtz. Write them out (in all their beauty). Don’t forget the integration boundariesThe electric field has been measured to be horizontal and to the right everywhere on the closed box as shown in the figure below. All over the left side of the box Ej = 107 V/m, and all over the right (slanting) side of the box E2 = 358 V/m. On the top the average field is E3 = 160 V/m,on the front and back the average field is E4 = 180 V/m, and on the bottom the average field is E5 = 200 V/m. E3 E1 12 cm E2 E4 5 cm Es 18 cm How much charge is inside the box?
- Class: Electromagnetics Consider a fixed hollow spherical shell with radius R and surface charge +? (sigma). A particle with mass m and charge -Q that is initially at rest falls in from infinity. Assume that a tiny hole has been cut in the shell to let the charge through. Determine the speed of the particle when it reaches the center of the shell. Your answer should be a function of ? (sigma), Q, and m.M6In addition to the cosmic background radiation of photons, the universe is thought to be permeated with a background radiation of neutrinos (v) and antineutrinos (v ), currently at an effective temperature of 1.95 K. There are three species of neutrinos, each of which has an antiparticle, with only one allowed polarization state for each particle or antiparticle. For parts (a) through (c) below, assume that all three species are exactly massless. Derive a formula for the number of neutrinos per unit volume in the neutrino background radiation. Evaluate your result numerically for the present neutrino temperature of 1.95 K.