Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 4, Problem 4.16P
A spherically symmetric charge distribution in free space (with a < r < so) is known to have a potential function V(r) = V0a2/r2, where V0 and a are constants, (a) Find the electric field intensity. (b) Find the volume charge density. (c) Find the charge contained inside radius a. (d) Find the total energy stored in the charge (or equivalently, in its electric field).
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Chapter 4 Solutions
Engineering Electromagnetics
Ch. 4 - Given E = Exax + Eyay + Ez3z V/m, where EX, Ey,...Ch. 4 - A positive point charge of magnitude q1 lies at...Ch. 4 - Given E=Epap+Ea+Ez+azV/m, where Ep, E and E2 are...Ch. 4 - An electric field in free space is given by...Ch. 4 - Consider the vector field G = (A/p) aa where A is...Ch. 4 - A electric field in free space is given as...Ch. 4 - Prob. 4.7PCh. 4 - Given E=-xax+yay,(a) find the work involved in...Ch. 4 - An electric field intensity in spherical...Ch. 4 - A sphere of radios a carries a surface density of...
Ch. 4 - At large distances from a dipole antenna (to be...Ch. 4 - Prob. 4.12PCh. 4 - Thee identical point charges of 4 pC each are...Ch. 4 - Given the electric field E=(y+1)ax+(x1)ay+2az find...Ch. 4 - Two uniform lines, 8 nC/m, are located at x=1, z=2...Ch. 4 - A spherically symmetric charge distribution in...Ch. 4 - Uniform surface charge densities of 6 and 2 nC/m2...Ch. 4 - Find the potential at the origin produced by a...Ch. 4 - Volume charge density is given as pv=poer/C/m3,...Ch. 4 - En a certain medium, the electric potential is...Ch. 4 - Prob. 4.21PCh. 4 - A Line charge of infinite length lies along the z...Ch. 4 - Prob. 4.23PCh. 4 - A certain spherically symmetric charge...Ch. 4 - Consider an electric field intensity in free space...Ch. 4 - Let us assume that we have a very thin, square,...Ch. 4 - By performing an appropriate Line integral from...Ch. 4 - Prob. 4.28PCh. 4 - A dipole having a moment P=3ax-5ay+10aznC.m is...Ch. 4 - Prob. 4.30PCh. 4 - A potential field in free space is expressed as...Ch. 4 - Prob. 4.32PCh. 4 - Prob. 4.33PCh. 4 - A sphere of radius a contains volume charge of...Ch. 4 - Four 0.8 nC point charge are located in free space...Ch. 4 - Surface charge of uniform density ps lies on a...
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- An FDM is used to multiplex two groups of signals using AM-SSB, the first group contains 25 speech signals, each has maximum frequency of 4 kHz, the second group contains 15 music signals, each has maximum frequency of 10 kHz. A guard bandwidth of 500 Hz is used bety each two signals and before the first one. 1. Find the BWmultiplexing 2. Find the BWtransmission if the multiplexing signal is modulated using AM-DSB-LC.arrow_forwardAn FM signal with 75 kHz deviation, has an input signal-to-noise ratio of 18 dB, with a modulating frequency of 15 kHz. 1) Find SNRO at demodulator o/p. 2) Find SNRO at demodulator o/p if AM is used with m=0.3. 3) Compare the performance in case 1) and 2).. Hint: for single tone AM-DSB-LC, SNR₁ = (2m²) (4)arrow_forwardFind Va and Vb using Nodal analysisarrow_forward
- 4. A battery operated sensor transmits to a receiver that is plugged in to a power outlet. The device is continuously operated. The battery is a 3.6 V coin-cell battery with a 245mAHr capacity. The application requires a bit rate of 36 Mbps and an error rate of less than 10^-3. The channel has a center frequency of 2.4 GHz, a bandwidth of 10 MHz and a noise power spectral density of 10^-14 W/Hz. The maximum distance is 36 meters and the losses in the channel attenuates the signal by 0.25 dB/meter. Your company has two families of chips that you can use. An M-ary ASK and an M-ary QAM chip. The have very different power requirements as shown in the table below. The total current for the system is the current required to achieve the desired Eb/No PLUS the current identified below: Hokies PSK Chip Set Operating Current NOT Including the required Eb/No for the application Hokies QAM Chip Set Operating Current NOT Including the required Eb/No for the application Chip ID M-ary Voltage (volts)…arrow_forwardUsing the 802.11a specifications given below, in Matlab (or similar tool) create the time domain signal for one OFDM symbol using QPSK modulation. See attached plot for the QPSK constellation. Your results should include the power measure in the time and frequency domain and comment on those results. BW 802.11a OFDM PHY Parameters 20 MHZ OBW Subcarrer Spacing Information Rate Modulation Coding Rate Total Subcarriers Data Subcarriers Pilot Subcarriers DC Subcarrier 16.6 MHZ 312.5 Khz (20MHz/64 Pt FFT) 6/9/12/18/24/36/48/54 Mbits/s BPSK, QPSK, 16QAM, 64QAM 1/2, 2/3, 3/4 52 (Freq Index -26 to +26) 48 4 (-21, -7, +7, +21) *Always BPSK Null (0 subcarrier) 52 subarriers -7 (48 Data, 4 Pilot (BPSK), 1 Null) -26 -21 0 7 21 +26 14 One Subcarrier 1 OFDM symbol 1 OFDM Burst -OBW 16.6 MHz BW 20 MHZ 1 constellation point = 52 subcarriers = one or more OFDM symbols 802.11a OFDM Physical Parameters Show signal at this point x bits do Serial Data d₁ S₁ Serial-to- Input Signal Parallel Converter IFFT…arrow_forwardFind Vb and Va using Mesh analysisarrow_forward
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