Wave motion in a medium
This program calculates the electric field in a material (ionic crystal or metallic plasma) as a function of position, z, and time, t. See Eq. 2.190 on page 46 of the notes. In this case we assume that the propagation vector, k, is
Problem Set 6 Fall 2008: Ionic Crystal.
(MathCAD program) provided for the ionic crystal, examine the form for E(z, t) in NaBr. [Note: the template is set up for KBr] Use a static dielectric constant = 5. 78, an optical dielectric constant:= 2. 64 and a t
Problem Set 5
Assignment 7: For a metal the electron density would be approximated by the fermi sea, 3 0 v 2 m v f v , v f 3 2 0 1/3 m h with m the effective mass of the electron. The equilibrium electron density for a charged plasma at temperature T is g
Problem Set 5
Assignment 7: For a metal the electron density would be approximated by the fermi sea, 3 0 v 2 m v f v , v f 3 2 0 1/3 m h with m the effective mass of the electron. The equilibrium electron density for a charged plasma at temperature T is g
Problem Set 4:
(Assignment 5) For a given system the electric field and current density are given by Assignment 5 z ct 2 cosk 0 z ct e 1 Er, t E 0 exp 2L 2 Jr, t J 0 exp z ct 2 2L 2 cosk 0 z ct 0 e 1
(a) Calculate the magnetic flux density, Br, t . (b) Ca
Problem Set 4:
(Assignment 5) For a given system the electric field and current density are given by Assignment 5 z ct 2 cosk 0 z ct e 1 Er, t E 0 exp 2L 2 Jr, t J 0 exp z ct 2 2L 2 cosk 0 z ct 0 e 1
(a) Calculate the magnetic flux density, Br, t . (b) Ca
Problem Set 3
(Jackson 6.20). 1. An example of the preservation of causality and finite speed of propagation in spite of the use of the Coulomg gauge is afforded by a unit strength dipole source that is flashed on and off at t = 0. The charge and current
Problem Set 3: 1. (Jackson 6.20). An example of the preservation of causality and finite speed of propagation in spite of the use of the Coulomb gauge is afforded by a unit strength dipole source that is flashed on and off at t = 0. The charge and current
Problem Set 2: 2.1 The Coulomb potential for a point charge located at r 0 is given by q (r , r 0 ) = |r r 0 | a) Find 2 (r, r 0 ) and write down the partial differential equation satisfied by (r, r 0 ). b) Using steps similar to those found on page 12 of
Problem Set 2: 2.1 The Coulomb potential for a point charge located at r 0 is given by q r, r 0 |r r 0 | a) Find 2 r, r 0 and write down the partial differential equation satisfied by r, r 0 . b) Using steps similar to those found on page 12 of Chapter 1
Wave motion in a medium
This program calculates the electric field in an ionic crystal (set for KBr) as a function of position, z, and time, t. See Eq. 2.190 on page 46 of the notes. In this case we assume that the propagation vector, k, is along the z di
Problem Set 6.
Assignment : Adapting the MathCAD program provided for the ionic crystal, examine the form for Ez, t in a plasma with 10 15 and P 10 as a function of o , the peak of the frequency distribution, E 0 . a) What is meant by the damping length?
Wave motion in a medium
This program calculates the electric field in a material (ionic crystal or metallic plasma) as a function of position, z, and time, t. See Eq. 2.190 on page 46 of the notes. In this case we assume that the propagation vector, k, is
Problem Set 8.
An antenna is constructed from conducting wire wrapped in the shape of a sphere with a current density given by J(r, t) = [ I 0 (r a) sin e i o t ]
a
= [J 0 (r)e i o t ] a) Set up the general expression for the vector and electrostatic pote
Problem Set 8.
An antenna is constructed from conducting wire wrapped around an insulaing sphere with a current density given by J(r, t) = [ I 0 (r a) sin e i o t ]
a
= [J 0 (r)e i o t ] a) Set up the general expression for the vector and electrostatic po
Problem Set 7.
(Adapted from Jackson 9.10) The transitional charge and current densities for the radiative transition from the m = 0, 2p state in hydrogen to the 1s ground state are (with the neglect of spin), (r, , , t) = 2e r exp( 3r )Y 00 Y 10 exp(i o
Problem Set 7.
(Adapted from Jackson 9.10) The transitional charge and current densities for the radiative transition from the m 0, 2p state in hydrogen to the 1s ground state are (with the neglect of spin), r, , , t 2e 4 r exp 3r Y 00 Y 10 expi o t; 2a o
Problem Set 1. (Fall 2006) The charge density for a hydrogenic p state can be written as r 2 exp r r, 2 3 e P 0 cos P 2 cos a0 a0 3 a 0 64 e 4. 8 10 10 statCoulomb, a 0 0. 529 10 8 cm. (a) Determine the multipole moments of this charge distribution and gi
Problem Set 1 1.1. The charge density for a hydrogenic p state can be written as r 2 exp r r, 2 3 e P 0 cos P 2 cos a0 3 a 0 64 a 0 e 4. 8 10 10 statCoulomb, a 0 0. 529 10 8 cm. (a) Determine the multipole moments of this charge distribution and give the
Chapter 2, page 34 details:
Thus, for a transverse electromagnetic wave to propagate in the medium the wave vector and angular frequency must satisfy the dispersion relation k 2 2 c or, using the dielectric function without damping, opt 2 T opt s opt 2 2
Chapter 2
Waves in Media
2.1 Introduction The propagation of waves in a medium depends on the magnetic permeability and electric permittivity functions ( ) and ( ) for the medium. We will generally deal with systems in which ( ) can be approximated as hav
Chapter 2
Waves in Media
2.1 Introduction The propagation of waves in a medium depends on the magnetic permeability and electric permittivity functions ( ) and ( ) for the medium. We will generally deal with systems in which ( ) can be approximated as hav
Chapter 2
Waves in Media
2.1 Introduction The propagation of waves in a medium depends on the magnetic permeability and electric permittivity functions ( ) and ( ) for the medium. We will generally deal with systems in which ( ) can be approximated as hav
In the cw mode the average power delivered to the currents by the fields is w(r ) = 1 T = =
T / 2 E(r, t ) J(r, t )dt T/2 1 e(r, ) j(r, ) 1 exp[i( + )t ]dt d d 2 T T / 2 (2 )
1 (2 ) 2 1 e(r, ) j(r, ) T
T/2
112 Let = ( + )
1 [exp(i T ) exp(i T )] d d 2 2
Chapter 1 Maxwells Equations, Conservation Laws
1.1
Maxwells Equations in Materials: D, H, P and M
Our starting point will be the experimentally deduced Maxwells Equations These consist of the four differential equations (in gaussian, cgs units) u G +u>w,