Fundamentals of Electromagnetics with Engineering Applications
5th Edition
ISBN: 9780471263555
Author: Stuart M. Wentworth
Publisher: John Wiley & Sons
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Chapter 4, Problem 4.32P
A magnetic field propagating in free space is given by
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Electromagnetics.
A spherical surface has following range.
Find volume of spherical surface.
An electric field propagates along the z-direction and has only one component along the x -axis. It can be generally described by the equation (phasor form):
Ex = E+ exp (-jbz) + E- exp (+jbz)
At z=0, there is a mirror (perfect conductor); using the boundary condition Ex =0 at z=0, find:
The relation between E- and E+ , also known as the “reflection coefficient”.
The time expression of the total electric field for z < 0, assuming an angular frequency w.
The distance between the maxima and minima of the electric field.
(THIS PROBLEM IS ENTIRELY EQUIVALENT OF AN IDEAL TRANSMISSION LINE SHORT-CIRCUITED AT Z= 0).
The axis of a circular cylinder coincides with the z-axis and it rotates with an angular velocity of (3i−5j +9k) rad/s. Determine
the tangential velocity at a point P on the cylinder,
whose co-ordinates are ( j +5k) metres,
the magnitude of the tangential velocity
iii. Derive the electromagnetic wave equation considering a region with no charges and currents, such as in a vacuum.
Chapter 4 Solutions
Fundamentals of Electromagnetics with Engineering Applications
Ch. 4 - How long does it take for charge density to drop...Ch. 4 - At a particular point in a slab of silver, a...Ch. 4 - A current density is given by J=e.01taA/m2. Find...Ch. 4 - At t=0s, 60.0C is evenly distributed throughout a...Ch. 4 - A propagating electric field is given by...Ch. 4 - A 10.0-MHz magnetic field travels in a fluid for...Ch. 4 - Modify the simple wave program in MATLAB 4.1 to...Ch. 4 - Modify the traveling wave program in MATLAB 4.2 to...Ch. 4 - Prob. 4.9PCh. 4 - A bar magnet is dropped through a conductive ring....
Ch. 4 - Considering Figure 4.7, suppose the area of a...Ch. 4 - Sometimes a transformer is used as an impedance...Ch. 4 - Prob. 4.13PCh. 4 - The mean length around a nickel core of a...Ch. 4 - A triangular wire loop has its vertices at the...Ch. 4 - Referring to Figure 4.23, suppose a conductive bar...Ch. 4 - Suppose we have a conductive bar moving along a...Ch. 4 - The radius r of a perfectly conducting metal loop...Ch. 4 - Rederive Vemf for the rectangular loop of Figure...Ch. 4 - In Figure 4.16, replace the rectangular loop with...Ch. 4 - Prob. 4.21PCh. 4 - Prob. 4.22PCh. 4 - A Faraday disk generator is similar to the...Ch. 4 - Prob. 4.24PCh. 4 - Prob. 4.25PCh. 4 - Suppose a vector field is given by A=2cosaz Verify...Ch. 4 - A pair of 60cm2 area plates are separated by a...Ch. 4 - Plot the loss tangent of seawater ( =4S/m and r=81...Ch. 4 - A 1.0-m-long coaxial cable of inner conductor...Ch. 4 - Suppose in free space that E(z,t)=5.0e2ztaxV/m. Is...Ch. 4 - An electric field propagating in a lossless...Ch. 4 - A magnetic field propagating in free space is...Ch. 4 - Find the instantaneous expression for E for the...Ch. 4 - Given, at some point distant from a source at the...Ch. 4 - In a lossless, nonmagnetic media, the magnetic...Ch. 4 - Suppose, in a nonmagnetic medium of relative...Ch. 4 - Prob. 4.37PCh. 4 - Prob. 4.38PCh. 4 - Prob. 4.39PCh. 4 - Find E(z,t) in Problem 4.32 using phasors.Ch. 4 - Prob. 4.41PCh. 4 - Find H(y,t) in Problem 4.36 using phasors.Ch. 4 - In MATLAB 4.4, a polar plot of the phasor...
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- Electromagnetics Given the field D =3zp cos(φ) aφ. Determine DivD at P(p=2.6, φ=1.9, z=-3)arrow_forwardConsider the dipole in the figure below with the charge magnitude of q = 3.0 nC and separation distance d = 4.0 cm. What is the potential at the following locations in space? (a) (0, 0, 1.0 cm); (b) (0, 0, –5.0 cm); (c) (3.0 cm, 0, 2.0 cm).arrow_forwardCalculate numerical values for V and rho v at point P, in free space if: I= 2 cos phi r^ 2 ,at P(r P(r = 0.5, theta = 45 ^ o, phi = 60 degrees) ; (b) V = 5r ^ 2 * cos 2phi (a) V , at P(r = 3, phi = pi / 3, z = 2) .arrow_forward
- Electromagnetics: - Give the rectangular coordinates of the point C (ρ = 4.4, φ = −115◦, z = 2).arrow_forward1. Polarization a. causes charging by induction b. redistributes charges c. affects dielectrics d. all of the above 2. Around a dipole, the electric field lines a. originate from the negative to the positive charge b. hit the equipotential surfaces at any angle c. form a vector field d. form a scalar field 3. Plots of potential V (vertical axis) as a function of distance (horizontal) a. are on the positive V side of the horizontal for a positive charge b. are on the negative V side for a negative potential c. could be different for many charges d. all of the above 4. When moving from point A to B to calculate potential difference, a. the result is dependent on the path taken b. the increase or decrease in potential energy does not depend on the path c. you may go to infinity then come back d. all of the abovearrow_forwardobtain the spherical coordinates of 10a, at the point p(x 3.y 2,24). with unit vectorarrow_forward
- A magnetic field strength of 7 μA/m is required at a point on θ= π/2, 4 km from an antenna in the air. Neglecting Ohmic loss, Calculate the current if it is a Half-wave dipole? 185.9 mA 195.9 mA 165.9 mA 175.9 mAarrow_forwardWe are given the non-uniform field E = y ax + x ay + 2 az and we are asked to determine the work expended in carrying 2C from B (1, 0, 1) to A (0.8, 0.6, 1) along the shorter arc of the circle x2 + y2 = 1, z = 1.arrow_forwardPlot the point with spherical coordinates (8, π/3, π/6) and express its location in both rectangular and cylindrical coordinates.arrow_forward
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