Fundamentals of Electromagnetics with Engineering Applications
1st Edition
ISBN: 9780470105757
Author: Stuart M. Wentworth
Publisher: Wiley, John & Sons, Incorporated
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Textbook Question
Chapter 2, Problem 2.18P
A segment of line charge
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Four point charges are at the corners of a square of side 10 cm, asshown in the following figure. If q1 = q2 = q4 = 3.2 × 10−10C and q3 = 1.6 ×10−10C , find the electric field at point P, the center of the square, in unit-vector and magnitude-angle notation.
Boundary Conditions
Two planar slabs of equal thickness but with different dielectric constants are shown inFigure. Eo in air makes an angle of 30° with the z-axis.
Calculate the angle that E makes with the z-axis in each of the two dielectric layers.
Chapter 2 Solutions
Fundamentals of Electromagnetics with Engineering Applications
Ch. 2 - Given P(4, 2, 1) and APQ=2ax+4ay+6az, find the...Ch. 2 - Prob. 2.2PCh. 2 - Prob. 2.3PCh. 2 - Suppose Q1(0.0,-3.0m,0.0)=4.0nC,...Ch. 2 - Prob. 2.5PCh. 2 - Suppose 10.0nC point charges are located on the...Ch. 2 - Four 1.00nC point charges are located at...Ch. 2 - A 20.0nC point charge exists at...Ch. 2 - Prob. 2.9PCh. 2 - Convert the following points from Cartesian to...
Ch. 2 - Prob. 2.11PCh. 2 - Prob. 2.12PCh. 2 - Prob. 2.13PCh. 2 - A 20.0–cm–long section of copper pipe has a...Ch. 2 - A line charge with charge density 2.00nC/m exists...Ch. 2 - You are given two z–directed line charges of...Ch. 2 - Suppose you have a segment of line charge of...Ch. 2 - A segment of line charge L=10.nC/m exists on the...Ch. 2 - In free space, there is a point charge Q=8.0nC at...Ch. 2 - Prob. 2.20PCh. 2 - Sketch the following surfaces and find the total...Ch. 2 - Consider a circular disk in the x–y plane of...Ch. 2 - Suppose a ribbon of charge with density S exists...Ch. 2 - Sketch the following volumes and find the total...Ch. 2 - You have a cylinder of 4.00–in diameter and...Ch. 2 - Consider a rectangular volume with...Ch. 2 - Prob. 2.27PCh. 2 - Prob. 2.28PCh. 2 - Given D=2a+sinazC/m2, find the electric flux...Ch. 2 - Suppose the electric flux density is given by...Ch. 2 - Prob. 2.31PCh. 2 - A cylindrical pipe with a 1.00–cm wall thickness...Ch. 2 - Prob. 2.34PCh. 2 - Prob. 2.35PCh. 2 - A thick–walled spherical shell, with inner...Ch. 2 - Prob. 2.37PCh. 2 - Determine the charge density at the point...Ch. 2 - Given D=3ax+2xyay+8x2y3azC/m2, (a) determine the...Ch. 2 - Suppose D=6cosaC/m2. (a) Determine the charge...Ch. 2 - Suppose D=r2sinar+sincosaC/m2. (a) Determine the...Ch. 2 - Prob. 2.42PCh. 2 - A surface is defined by the function 2x+4y21nz=12....Ch. 2 - For the following potential distributions, use the...Ch. 2 - A 100nC point charge is located at the origin. (a)...Ch. 2 - Prob. 2.46PCh. 2 - Prob. 2.47PCh. 2 - Prob. 2.48PCh. 2 - Suppose a 6.0–m–diameter ring with charge...Ch. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - The typical length of each piece of jumper wire on...Ch. 2 - A 150–m length of AWG–22 (0.644 mm diameter)...Ch. 2 - Determine an expression for the power dissipated...Ch. 2 - Find the resistance per unit length of a stainless...Ch. 2 - A nickel wire of diameter 5.0 mm is surrounded by...Ch. 2 - Prob. 2.57PCh. 2 - A 20nC point charge at the origin is embedded in...Ch. 2 - Suppose the force is very carefully measured...Ch. 2 - The potential field in a material with r=10.2 is...Ch. 2 - In a mineral oil dielectric, with breakdown...Ch. 2 - Prob. 2.62PCh. 2 - For z0,r1=9.0 and for z0,r2=4.0. If E1 makes a 300...Ch. 2 - Prob. 2.64PCh. 2 - Consider a dielectric–dielectric charge–free...Ch. 2 - A 1.0–cm–diameter conductor is sheathed with a...Ch. 2 - Prob. 2.67PCh. 2 - For a coaxial cable of inner conductor radius a...Ch. 2 - Prob. 2.69PCh. 2 - Prob. 2.70PCh. 2 - A parallel–plate capacitor with a 1.0m2 surface...Ch. 2 - Prob. 2.72PCh. 2 - Prob. 2.73PCh. 2 - Given E=5xyax+3zaZV/m, find the electrostatic...Ch. 2 - Suppose a coaxial capacitor with inner radius 1.0...
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- Three charge distributions as follows: a uniform sheet at x=0 m with ps1 = (/31) nC/m2, a uniform sheet at x 4 m with Ps2 (-137) nC/m2, and a uniform line at x= 6 m, y 0 m with p -2 nC/m. The E at (2, 0, 8) m is:arrow_forwardProblem 4. = 5 [nc] is on the x-axis at x₁ = -1 [m] and a second positive point charge q₂ = 5 [nc] is on the x-axis at x₂ = 3 [m]. a. Point A. d1 = b. |Ē₁A| = Point A is on the x-axis at XÃ = 7 [m]. Ẻ₁A d. Point A. d2 = e. = E2Al 2A C. by the charge q₁ at Point A. i + [N/C] Find the distance between 92 and 0 = = O+x O-x O+y O-y A positive point charge q₁ 2 92 Find the distance between q₁ and m Find the magnitude of E₁A [N/C] m f. by the charge q₂2 at Point A. Calculate ₁4 the electric field created 1A [N/C] g. Consider a point located 6 m from the origin, what will be the direction of the net electric field created by the charges at this point? 2 + x, m Find the magnitude of È 2A. [N/C] Calculate E24 the electric field created 2Aarrow_forwardAn infinite line charge of (2 µC/m )are located on the z -axis. Electric field due to thisline charge at point (- 2, - 1,5) will bearrow_forward
- Two charges qa=5uc and qb=8.5 uc are separated by a distance of 15 cm. point p is located along the line segment joining two charges. how far is point p from qa if the magnitude of the electric field at poin p due to the two charges is equal to zero? Draw a sketch of the problem and label appropriatelyarrow_forwardWhich of the following statements is correct? Select your answer. Take the surface integral and divide its line integral to solve the charge with a given line charge density. Take the double integration procedure to solve the charge with a given surface charge density. Take the line integral first, then the surface integral to solve the charge with a given volume charge density. Divide the volume charge density by the surface charge density to solve the charge.arrow_forward..........gsgsarrow_forward
- A solid conducting sphere of radius R carries a charge +Q. A thick conducting shell is concentric with the sphere and has an inner radius R2 and outer radius R3. The shell carries a charge -Q. The figure shows a cross section. a) Where are the charges located? Add charge symbols to the figure. R1 R3 R2 b) Add a few electric field lines and equipotential lines to the figure. Please label the lines clearly. c) Draw a sketch of the potential as a function of distance from the center of the sphere. Please label all interesting points on the graph.arrow_forward(al:Determine E caused by the spherical cloud of electrons with a volume charge density of - 1.68 x 10 -18 for 0 10mm. Clearly mention the surfaces, there differential components and write the equation properly by doing all the steps. (b): For the dielectric composition shown in the figure find out its total capacitance.arrow_forwardAn air filled parallel plate capacitor is arranged such that the upper plate carries surface charge density 2C/m² and lower plate carries surface charge density -2C/m? as shown in figure. The electric field intensity over the top plate will bearrow_forward
- A non-uniform charge density of P = -x [inc/m], are distributed on the x-axis Find Ẽ at p (0₂0₂2) from x=-4 to x=4. Find È at Earrow_forwardUniform line charges of 0.4 µC/m and –0.4 µC/m are located in the x = 0 plane at y = -0.6 and y = 0.6 m, respectively. Find E at R(2, –3, 4). %3D Select your answer. N (626.35az – 242.19a,) V (-625.8a, – 241.6a,) m V (-625.8a, + 241.6a,) m N (626.35а, + 242.19а,)arrow_forwardGiven a 2.215 nC/m2 surface charge at z = – 15. Solve E on point (250, 100, 10) caused by the surface charge in (nC/m).arrow_forward
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