1. Show if the following field is a Maxwellian equation (If it satisfy the 1st and...
Part # II: (2 Marks) An EM field is said to be nonexistent or not Maxwellian if it fails to satisfy Maxwell's equations and the wave equations derived from them. Using the answers in part 1, show that the following magnetic field in a certain dielectric material satisfies all Maxwell's equations (part a) and find the corresponding phase constant B (part b). The magnetic field is given by H(y,t) = 5 cos (2nft + By)a, A/m for which = 480,...
(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...
1. The time-dependent Schrödinger equation The time-dependent Schrödinger equation is -R2 824(1,t) + V (1,t) (1,t) = in 2m 0:2 . (a) For V1, t) = 0, show that the wave function (1,t) = A sin (kr - wt) does not satisfy the time- dependent Schrödinger equation. (b) For VI,t) = 0, Show that I, t) = A cos(kr - wt) + i sin (kr - wt) does satisfy this equation. This is a simple demonstration that the wavefunction in...
HELP with E-FIELDS.. please fully explain bc this question
confuses me
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3. The electric field and magnetic field components of a signal propagating in free space are given by E(z,t)-nHo cos(7.5x10 t-Bz)a H(z,t)- H,cos(7.5x10't-Bz)a, Find the values of β and η such that these expressions satisfy all of Maxwell's equations. OD OB (Hint: Use first and xE- to find β and 17, then show that the above c, a fields also satisfy V-D 0 and V B-0).
Show that the electric field: E(x,t)-E cos(kr-at)+E, cos(kx-of) satisfies Maxwell's equation: Here, ø, and oj are two arbitrary frequencies, and remember oj-ck, and oj-ck quencies, and remember: ai-ck, and arch.
Question 1: As you work through the parts of this question you are going to show that the Maxwell equations naturally contain electromagnetic waves. In a region of space that is void of all charges and currents, p=0 and J = 0 the Maxwell equations come out to be: Y E = 0 7.B=0 7 x Ē = -1 1 x B = Poco a) Using the same idea as I did in the lecture, derive the Wave Equation for...
1. (5 points) This course deals with Maxwell's equation. When there is no chargeor current, the electric field E and the magnetic field intensity satisfy Use identities from vector calculus to show that these imply เอ2 1 02 where c is the velocity of light in vacuum. Find the connection between cand ,10, eo. You may assume all partial derivatives commute
#4
3. Demonstrate that the following equations satisfy the "wave equation." For those that do, find the wave amplitude, wave speed, wavenumber, wavelength, angular frequency, and frequency in Hz? Also, denote if the wave is rightward or leftward travelling. c. y(x,t) 6cos(3x+18t) d. y(x,t) -3tan(6x+60t) yx,t) -6cos(67x)cos(80t) e. 4. For the equation given in 3(a), plot the response using a PC as a function of x over at least two full wavelengths at r-0.1 second. On a different plot, show...
Show that solutions to Maxwell’s equations (for E⃗ and B⃗ ) satisfy the wave equation, thus predicting that the solutions (EM waves) are in fact traveling waves.With what speed do the waves travel?