Electromagnetic Theory

13. An L-R-C series circuit is connected to an AC-source of constant voltage amplitude ΔU0 and variable angular frequency ω. a) At what angular frequency is the voltage amplitude across the resistor R at maximum? b) At what angular frequency is the voltage amplitude across the capacitor C at maximum? c) At what angular frequency is the voltage amplitude across the inductor L at maximum? See attached file for full problem description. Only #13

Electromagnetic Theory Question

Electromagnetic radiation is emitted by accelerating charges. The rate at which energy E is emitted from charge q moving with acceleration a is given by ,where c is the speed of light. a) Verify that this equation is dimensionally correct. b) If a proton with a kinetic energy of 6 MeV is traveling in a particle accelerator in a circular orbit of radius 0.75 m, what fraction of its energy does it radiate per second? c) If the electron in a hydrogen atom can be considered to be in a circular orbit with radius of 0.0529 nm and kinetic energy of 13.6 eV, how much energy would it radiate per second? (What does it tell you about the use of classical physics in describing the atom?) See attach... click for more

Electromagnetic Theory

15. Electromagnetic waves propagate much differently in conductors than they do in dielectrics and vacuum. If the resistivity ρ of the conductor is sufficiently low (that is, if it is a sufficiently good conductor), the oscillating electric field of the wave gives rise to an oscillating conduction current that is much larger than the displacement current. In this case, the wave equation for an electric field E(x,t) = Ey(x,t) j propagating in the +x-direction within a conductor is given by , where μ is the permeability of the conductor. a) Prove that solution for this equation is and define k. b) Explain why electric field exponentially decreases in amplitud... click for more

The theory of special relativity and E = m c^2.

I need to understand some basic things about relativity and the equation E=mc^2. So I would like a clear discussion of Einstein's relation E=mc^2 for the rest energy of a particle. I want an argument supporting the interpretation of mc^2 as the particle's energy. Please describe some consequences of this identification. Also why should anyone believe E=mc^2?

Cathode ray/cylindrical electrostatic analyzer

Cathode ray/cylindrical electrostatic analyzer. See attached file for full problem description.