Fundamentals of Electromagnetics with Engineering Applications
1st Edition
ISBN: 9780470105757
Author: Stuart M. Wentworth
Publisher: Wiley, John & Sons, Incorporated
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Chapter 3, Problem 3.31P
To determine
The magnetic flux that passes along the z -axis for an infinite coaxial cable.
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From two homogeneous media; Express as Νr1=2 for x<0 region and ,Nr2=72 for x>0 region is being done. Expression of magnetic field in primary medium H = 150x − 400y + 250z A/m as it is;
a) Calculate the expression for the magnetic field in the second medium.
b) Calculate the magnetic flux density in the primary medium.
c) Calculate the magnetic flux density in the second medium.
An image taken from the cross-sectional area of a coaxial cable consisting of a solid inner conductor of Radius R, surrounded by a concentric cylindrical tube of inner radius R, and outer radius Rg is given in the figure. The inner conductor and outer conductor (cylindrical tube) have the current density j1 = Cr and ja = Cyr respectively, for which r is the radial distance from the center. Each conductor carries the same total 1, in opposite directions. What is the magnitude of the magnetic field B, at a distance 11 = 2 cm and B, at a distance 12 = 9 cm? (R = 5 cm; R2 = 8 cm; Rg = 10 cm: 1, = 4 A; Ho = 47x10-?T.m/A. Take the sign of the current coming out from the page plane as positive).
A 2a-part piece of wire was removed from the middle area of my upper edge, consisting of rectangular conductive wires with a long edge of 10a and a short edge of 4a, and replaced with a semicircular conductive wire with a radius. A constant I current passes through the closed ring in the way. What's the magnetic field vector at that point? (Get T=3).
Chapter 3 Solutions
Fundamentals of Electromagnetics with Engineering Applications
Ch. 3 - Find AB for the following: A=2ax3ay+4az,B=5ay1az...Ch. 3 - Prob. 3.2PCh. 3 - Given the vertices of a triangle...Ch. 3 - A segment of conductor on the z–axis extends...Ch. 3 - Prob. 3.5PCh. 3 - Prob. 3.6PCh. 3 - A square conductive loop in the shape 10.0 cm is...Ch. 3 - A conductive loop in the x–y plane is bounded by...Ch. 3 - How close do you have to be to the middle of a...Ch. 3 - For the ring of current described in MATLAB 3.2,...
Ch. 3 - A solenoid has 200 turns, is 10.0 cm long, and has...Ch. 3 - For the solenoid of the previous problem, plot the...Ch. 3 - Prob. 3.13PCh. 3 - Two infinite extent current sheets exist at z=2.0m...Ch. 3 - An infinite extent current sheet with K=6.0ayA/m...Ch. 3 - Given the field H=3y2ax, find the current passing...Ch. 3 - Given a 3.0–mm–radius solid wire centered on...Ch. 3 - Given a 2.0–cm–radius solid wire centered on...Ch. 3 - An infinitesimally thin metallic cylindrical shell...Ch. 3 - A cylindrical pipe with a 1.0–cm wall thickness...Ch. 3 - Prob. 3.21PCh. 3 - Prob. 3.22PCh. 3 - Consider the toroid in Figure 3.55 that is tightly...Ch. 3 - Find A for the following fields: A=3xy2/zax...Ch. 3 - Find J at (3m,60,4m) for H=(z/sin)a(2/cos)azA/mCh. 3 - Suppose H=y2ax+x2ayA/m .(a) Calculate HdL around...Ch. 3 - Prob. 3.27PCh. 3 - Suppose you have the field H=rcosaA/m. Now...Ch. 3 - Prob. 3.29PCh. 3 - Suppose an infinite extent sheet of current with...Ch. 3 - Prob. 3.31PCh. 3 - A 1.0nC charge with velocity 100.m/s in the y...Ch. 3 - A 1.0nC charge with velocity 100.m/s in the z...Ch. 3 - A 10.nC charged particle has a velocity...Ch. 3 - What electric field is required so that the...Ch. 3 - An electron (with rest mass Me=9.111031kg and...Ch. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - Suppose you have a pair of parallel lines each...Ch. 3 - In Figure 3.57, a 2.0-A line of current is shown...Ch. 3 - Modify MATLAB 3.4 to find the differential force...Ch. 3 - Prob. 3.43PCh. 3 - A square loop of 1.0-A current of side 4.0 cm is...Ch. 3 - A current sheet K=100axA/m exists at z=2.0cm. A...Ch. 3 - Prob. 3.46PCh. 3 - Prob. 3.47PCh. 3 - A solid nickel wire of diameter 2.0 mm evenly...Ch. 3 - Prob. 3.49PCh. 3 - The plane y = O separates two magnetic media....Ch. 3 - Prob. 3.52PCh. 3 - Prob. 3.53PCh. 3 - Prob. 3.54PCh. 3 - Prob. 3.55PCh. 3 - Prob. 3.56PCh. 3 - Prob. 3.57PCh. 3 - Prob. 3.58PCh. 3 - Prob. 3.59PCh. 3 - Prob. 3.60PCh. 3 - Prob. 3.61PCh. 3 - In Figure 3.59, a 2.0-cm-diameter toroidal core...Ch. 3 - Suppose the 2.0-cm-diameter core of the toroid in...Ch. 3 - Prob. 3.64PCh. 3 - Consider a 1.0-mm air gap in Figure 3.49a. The...
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- A flat, circle surface area with a radius of 4m is in the YZ-plane at x=0, Find the magnitude of the magnetic flux through this surface produced by a magnetic flux density of B=3.5ax-6.4ay+8az Tarrow_forwarda) A circular loop of radius ? carries current ? as shown in the figure. Find the magnetic flux density ?⃗ at a point on the axis of the loop by using Biot-Savart law. Show all the details of Biot-Savart formulation b) A surface charge density exists on the hemispherical surface of the radius ? shown in the figure given as??⃗⃗ =?0????ê?A/m where ?0 is constant. i) Find the total current flowing on the surface ii) Using the solution of part (a), find the magnetic flux density ?⃗ at the origin ?.arrow_forwardThe magnetic field intensities inside and outside of a long and smooth conductor with a cross section radius are as follows. Accordingly, find the current densities J inside and outside the conductor. (Hint: Use cylindrical coordinates)arrow_forward
- A long, solid, cylindrical wire of radius A has a current density given by j = j0r/A. Determine the magnetic field, within the wire, in terms of the total current "I" flowing through the wire.arrow_forwardAn infinitely long wire carrying current is extended along the z-axis. A square plate with edge length a, lying in the yz plane, is placed next to the wire. Find the magnetic flux passing through the plate surface.arrow_forwardA current with a constant current density of Js=1π (A/m2 ) in the +z direction from the radius wire, and from the infinitely long cylindrical shell with inner radius b=3m and outer radius c=4m, constant I=4 Amperes homogeneously distributed in the cross section in the −z direction current is flowing. Accordingly, using the Ampere formula, calculate the magnetic field in regions r<a,a<r<b,b<r<c and r>c.arrow_forward
- The flux density within the cylindrical volume bounded by r = 5m, z = 0 and z = 2 m is given by, D=30 eta-2 z a, C/m². what is the total outward flux crossing the surface of the cylinder?arrow_forwardThe magnetic flux density in all of space is given by B=(3z)ax+(8x2−x2y)ay+(y+x2z)az Wb/m2. Let S denote the paraboloidal surface defined by y=x2+z2,0≤y≤64. Find the net magnetic flux Φ passing through S in the direction away from the xz-plane. Hint: Think about whether there is another way to solve this, such as by using a capping surface.arrow_forwardIn the upper half space, which is the empty space, I = 7 A current flows from the infinitely long wire along the y axis that intersects the z axis at the point C (0,0,10). Half-space z <0 is from a material with relative magnetic permeability µr = 5. Magnetic field in terms of given magnitudes Hx + Hy + Hz =? write it numerically.arrow_forward
- Q1) Evaluate both sides of stoke's theorem if the magnetic flux density is given by 37.7r aphi(vector) uWb/m^2 in a free space area defined byr = 3; 0arrow_forwardUsing Gauss’ law deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point (i) outside and (ii) inside the shell. Plot a graph showing variation of electric field as a function of r > R and r < R (r being the distance from the centre of the shell)arrow_forwardConsider a transmission line of three wires (infinite length). Each of the wires has a radius of 2 cm. Wire #1 whose center is at the point (0.0) cm flows a current of 3 A, through wire #2 centered at (0.10) cm a current of 5 A flows in the same direction as conductor 1 and Wire #3 centered at (0,-10) cm carries a current of 7 A in the opposite direction from conductors #1 and #2. Find the intensity and density of the magnetic field at the point P(3,0).arrow_forward
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The Biot-Savart Law; Author: Jennifer Cash;https://www.youtube.com/watch?v=1BoIH6Quhiw;License: Standard Youtube License