Concept explainers
Consider the following time-varying current density, which is in the form of a propagating wave at frequency f, traveling at velocity v (more about this in Chapter 10):
where J0, is a constant amplitude, đ�œ” = 2đ�œ‹f is the radian frequency, and & is a constant to be found. Determine β as a function of đ�œ” and v such, that the given waveform satisfies both Eqs. (3) and (5). Begin with Eq. (5).
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Engineering Electromagnetics
- 1) A lightwave is propagating in the y-axis of a Cartesian coordinate system and it is polarized in the z direction. It is known that the wave propagating with a half speed of free space propagation, its wavelength is green (500 nm) before entering the medium characterized by refractive index, n. The light power intensity is carried by the wave 100 mW/m^2. a) Draw a Cartesian coordinate system showing the wave propagation with k-wave vector, Also, show the Electrical and Magnetic fields on the drawing b) Calculate the k (wave vector) and W (angular frequency) for given numerical values,Find the wave amplitudes in the medium d) Write down the complete mathematical expression for the lightwave described in detail abovearrow_forwardGiven that D = 10sinϴar + 2 cosϴaϴ .Evaluate both sides of the divergence theorem for the volume enclosed by the shell r = 2.arrow_forwardA rectangular frame with the dimensions a=1.7 m, b=1.5 m is located on the xy-plane with its center at the origin as shown in the below figure. An electromagnetic wave with an induction field of B vector =0.6cos(2πt)az(vector) T exists. Calculate V0 if the electromotive force is in the form of e(t)=V0sin(2πt) voltsarrow_forward
- 6.2 In a microwave range measurement system the electromagnetic signal v1 ¼ A sin 2ft, with f ¼ 100 MHz, is transmitted and its echo v2ðtÞ from the target is recorded. The range is com- puted from , the time delay between the signal and its echo. (a) Write an expression for v2ðtÞ and compute its phase angle for time delays 1 ¼ 515 ns and 2 ¼ 555 ns. (b) Can the distance be computed unambiguously from the phase angle in v2ðtÞ? If not, determine the additional needed information. (a) Let v2ðtÞ ¼ Bsin 2f ðt Þ ¼ B sinð2ft - Þ. For f ¼ 100 MHz ¼ 108 Hz, - ¼ 2f ¼ 2 108 ¼ 2k þ where 0arrow_forwardA rectangular waveguide with dimensions a = 5cm, b = 4.2cm will operate below 4.5Ghz. if it is filled with a medium characterized by o = 0 e = 3E0 Ur = 2 How many TE and TM modes can I transmit? Calculate the cutoff frequency of the nodesarrow_forwarda medium is characterized by σ= 0, μ= 2μ0,, and ε= 5ε0. if H = 2 cos (wt — 3y) az, a/m, calculate E.arrow_forward
- Two identical loudspeakers are located at points (−10, 0, 0) and (0, 0, 10) of our coordinate system, where the numbers in the brackets correspond to the (x, y, z) coordinates of the points, expressed in meters. The loudspeakers are driven by the same oscillator with a frequency of 170 Hz. The speed of sound in air can be considered 340 m/s. a) Give the coordinates of those points located on the positive x axis where the sound waves coming from the two loudspeakers interfere constructively. b) A receiver is started to move slowly from the origin (0, 0, 0) along a path lying in the x–y plane so that it receives constant sound intensity throughout its slow motion. What is the shape of the path the receiver should take?arrow_forwardThere are point loads ,Q1 = 5, Q2 = 8 and Q3 = 6 at points A(-8,0), O(0,0) and B (6,0) in the OXY plane, respectively. Write the value of the x-component of the electric field in ke numerically at the point P(0, 10) on the-axis.arrow_forwardIn free space ⃗?⃗ (?, ?) = 70cos(?? − ??)⃗?⃗ (V/m). Find the average power crossing a circular area of radius 2 meters in a plane ? = 0.arrow_forward
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