6. Frequency dependence of the electrical conductioily. Use the equation midoldt +uh)--eE for the electron drift...
12. Use the equation midv/dt +v/t)=-eE for the electron drift velocity, v, to show that the conductivity at frequency, o is (0)= 1+ior 1+(or) Here a = ne' t/m is the DC conductivity. ii. What is plasma and what is meant by plasma frequency? Explain why satellites use the microwave range of frequencies for communication. For a frequency of 50 Gigahertz, what is the corresponding free space wavelength?
2. (i) The governing equation of motion for a single electron of mass m and charge -e moving with velocity y in uniform time-independent magnetic and electric fields is given by mayx B where B- (B, 0,0) di dr (a) Suppose the electron initially moves with velocity y (0,vo 0) in an electric field parallel to the magnetic field E-E-(E,00) By taking vf)-v +vi, where y i0, obtain v, and show that the speed vis constant. Describe (in words) the...
Quantum Physics 1. We'll use separation of variables to solve the Schrodinger equation in spherical geometry Show, that if the wave function takes the form 9(r,6, o) . R (r) (6)$(o) that the SchrodinDer equation can be separated in three equations d. (sin ) +1(1+1)sin2@62 ㎡Θ, and b) Show that imposing the boundary condition ф (ф)-ф (ф 2x) feguires that m-0, 1, 2, 3, ' . . dThe hrst few Legendre polymomials are given by 0-63-15 The "associated Legendre functions"...
an electron may freely move on a ring with a radius r, the schrodinger equation for this problem Problem 4 (2.0 points) An electron may freely move on a ring with a radius r. The Schrödinger equation for this problem is: 0=2/2 t? 2² 2mr2 2023 SV() = Ey() (4.1) where the azimuthal angle o characterizes the position of the electron. (a) A general form of the wave function is y (0) = A MO. (4.2) Show that Eq. (4.2)...
6. (12 points) The simplest (homogeneous, isotropic) 'Ohmic' materials are characterized by J=oE, where o is the constant) electrical conductivity (do not confuse it with the surface charge density!), and E is the electric field within the conductor. (a) (4 points Using the time-dependent form of the continuity equation, along with Ohm's law from above, derive a differential equation that describes the time and spa- tial dependence of the volume charge density par, t) within some conductor. Charac- terize (mathematically)...
E18M.6 The Rutherford model of the hydrogen atom (pro- posed by Ernst Rutherford in roughly 1910) imagines the electron as orbiting the proton in a circle (a) Use Newton's second law, Coulomb's law, and what you know about acceleration in circular motion to show that the electron's acceleration in a circular orbit of radius r is ã/(4me,mr) and its orbital kinetic energy is K-72/ (8πεο r), where e is the proton's charge and m is the electron's mass. (b) Show...
blem 6. Electromagnetic plane waves in a lossy medium tric field of an electromagnetic plane wave traveling in a lossy medium can be written as The where z is the distance, t is time, and fthe frequency. Forf- 1 GHz, it is found by measurement that the amplitude of the electric field is attenuated by a factor of 3 after the wave travels 100 m (ie, to 1/3 of the amplitude at: 0 when it arrives at : -100 m)....
Example 1 A star undergoes some mode of oscillation. Scientists/engineers have hypothesized that the oscillation frequency (cycles per second), o, is dependent on the density p and the radius R and the gravitational constant G which appears in Newton's law of universal gravitation. If you are not familiar with the gravitational constant, read the section on mass and weight in Chapter 4 (Dimensions/units) of the text. Therefore, w has dimensions (T), and P, R, Gare the governing parameters, with dimensions...
Electromagnetic plane waves in a lossy medium field of an electromagnetic plane wave traveling in a lossy medium can be written as 6. The where z is the distance, t is time, and f the frequency. For f 1 GHz, it is found by measurement that the amplitude of the electric field is attenuated by a factor of 3 after the wave travels 100 m (ie, to 130f the amplitude at z = 0 when it arrives at z-100 m)....
6-6 6-17 6-18 please help me, how could solve these problems In chemical kinetics and other types of rate processes, you frequently encounter with the initial condition m(0) == 2 6-4 B representing the interconversion of two species, A and B. The the scheme A rate equation for this interconversion can be written as dA/dt = -k\A + kąB, where k and kz are called rate constants. By conservation of mass, A(t)+B(t) = AoBo, where Aq = A(0) and Bọ...