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 3, Problem 3.62P
In Figure 3.59, a 2.0-cm-diameter toroidal core with
Figure 3.59 Toroid consisting of two types of magnetic material for Problem 3.62.
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A ferromagnetic core with a relative permeability of 1500 is shown in the given figure. The dimensions are as shown in the diagram, and the depth of the core is 5
cm. The air gaps on the left and right sides of the core are 0.050 and 0.070 cm, respectively. Because of fringing effects, the effective area of the air gaps is 5
percent larger than their physical size. If there are 300 turns in the coil wrapped around the center leg of the core and if the current in the coil is 1.0 A:
(a) What are the flux values for the left, center and the right legs of the core?
(b) What is the flux density in each air gap?
30 cm-
30 cm
7 cm
30 cm
0.07 cm
300 turns
0.05 cm
cm
Core depth - 5 cm
A ferromagnetic core with a relative permeability of 1500 is shown in the given figure. The dimensions are as shown in the diagram, and the depth of the core is 5
cm. The air gaps on the left and right sides of the core are 0.050 and 0.070 cm, respectively. Because of fringing effects, the effective area of the air gaps is 5
percent larger than their physical size. If there are 300 turns in the coil wrapped around the center leg of the core and if the current in the coil is 1.0 A:
(a) What are the flux values for the left, center and the right legs of the core?
(b) What is the flux density in each air gap?
7 cm
30 cm
30cm-
7 cm
30 cm
0.07 cm
300 turns
0.05 cm
7 cm
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Core depth - 5 cm
Figure 1 shows a ferromagnetic core with a relative permeability of 1850, the depth of the core
is 10 cm. The air gap on the core is 0.2 cm with effective area 5 % larger than their physical
size due to fringing effects. Given the number of turns N = 500 and current i = 2 x, where x is
the last digit of your student ID (example: EEE1705590, then i = 20 A):
(a) Find the total reluctance of the core and air gap. [CLO1-PL01:C2]
(b) Find the flux density of the air gap. [CLO1-PLO1:C2]
13 cm
23 cm
9 cm
5.6 сm
Air gap
31 cm
N turns
7 cm
Figure 1
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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