6. Given the total electromagnetic energy W (E.D+H. B) dv show from Maxwells equations that aw...
From physics, the total energy for this system is called the Hamiltonian and given by H(,vF(s) ds 0 In general, a numerical scheme will not conserve the energy of the system, i.e. H will not be constant. Suppose however that a trapezoidal method can be modified to produce an energy-conserving scheme. In particular assume the numerical scheme has the form where W is a yet-to-be-determined function, h is the time-step, and (yjl, {vj) denote the discretized position and velocity. Using...
(a) Show that this field can satisfy Maxwell's equations if w
and k are related in a certain way.
(b) Suppose w=1010s-1 and
E0=1kV/m. What is the wavelength? What is the energy
density in joules per cubic meter, averaged over a large region?
From this calculate the power density, the energy flow in joules
per square meter per second.
(c) Show also that the electric field of associated with a
spherically symmetric wave may have the dependence Ei =
{Acos[k(r...
(a) Show that this field can satisfy Maxwell's equations if w
and k are related in a certain way.
(b) Suppose w=1010s-1 and
E0=1kV/m. What is the wavelength? What is the energy
density in joules per cubic meter, averaged over a large region?
From this calculate the power density, the energy flow in joules
per square meter per second.
(c) Show also that the electric field of associated with a
spherically symmetric wave may have the dependence Ei =
{Acos[k(r...
10. a) Show that, for a system in equilibrium with constant internal energy, the first and second laws together require that dS P dv = 1 b) Determine as for an ideal gas. What are the dimensions of the answer? c) Does the answer to part b make sense given that equilibrium is also the state with the maximum value for the microscopic entropy, defined as S = kp log w?
For problems 6 to 10 An electromagnetic wave propagating in free space is given as E = 100e as H = H, e g where H is a magnitude and is a unit vector. . The magnetic field can be given Problem [6] <5 points> What is the direction of propagation? a) +x b) +y c) +z d) - e) - f) -Z Problem [7] <5 points> Calculate H Problem [8] <5 points> What is s in s. a) +x...
(e) Starting with the energy density of an electromagnetic field U = ε0E^2 /2 + B^2 /2µ0 and using two of Maxwell equations in free space, show that the rate of change of U is equal to the divergence of the Poyinting vector S, taken with the opposite sign, that is dU/dt = −∇ ∙ S
Given the electric field phasor E-E) ρ-le-jkza, in cylindrical coordinates, where 1.4 , show that it represents an electromagnetic wave propagating in free space by using (a) Maxwell's equations, and (b) Helmholtz equation. (c) Find the magnetic field phasor H. 88 8-9 Given the electric field phasor E -(E.a, +jE a)e n free space, determine (a) propagation direction, (b) H, (c) & and (d) polarization state. 1th yeaeo circularly polarized waves.
Given the electric field phasor E-E) ρ-le-jkza, in cylindrical...
c) Show that dVm by working from the total differential of the state function entropy S(T, Vm) and us- ing one of the Maxwell relations and the relationship linking the differential entropy dS and the heat capacity cv d) Using the differential entropy dS given or derived above, show that the reversible 2] isothermal expansion of a gas causes a change of the internal energy of the gas of by working from the differential form of the internal energy, e)...
6. The energy levels of a harmonic oscillator with angular frequency w are given by 2 (a) Suppose that a system of N almost independent oscillators has total energy E^Nhw 2 Mhw. Show that the number of states with exactly this energy equals the number of ways of distributing M identical objects among N compartments and that this number 1S MI(N 1) Hint: Consider the number of distinct arrangements of a set of M objects and N -1 partitions (b)...
can I have (b) please
e 2 (a) Consider an ionic crystal in w ich the repuisive potentbal energy Une arises from the action of the Paul exclusion principle, with U given by 8 The attractive potential energy per ion pair of opposite charges U.1s gven by In these expressions, r is the separation between the ions of opposite sign, n ss a large number and B a constant of the crystal Show that the total potential energy per ion-pair...