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 3.65P
Consider a 1.0-mm air gap in Figure 3.49a. The toroid mean radius and cross-sectional area are 50. cm and
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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
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Figure 1
A magnetic core with an airgap is shown in the figure below. The depth of the core is 7 cm, the length of the airgap in the core, g, is
0.04 cm, the relative permeability of the core is 2000. Assume a five percent increase in the effective air-gap area to account for
fringing. The reluctance of the air-gap in kAt/Wb is
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O b. 909.5
Oc. 90,95
O d. 866
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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 magnetic core with an air gap is shown below. For a relative permeability is 3500, and the space free permeability is 4TTX10-7 H/m. Find the reluctance of the left leg and the top side of the core. Ignore the gap in your calculations. 10 cm 0.1 cm gap 20 cm 5 cm 5 cm 40 cm 5 cm core depth = 10 cm Select one: O a. Rieft = 1251 A.t./Wb , Rtop = 1023 A.t/Wb O b. None O c. Rieft = 12.51 KA.t./Wb , Reop = 10.23 KA.t/Wb O d. Rieft = 125.1 A.t./Wb , Rtop = 102.3 A.t/Wbarrow_forwardQ4// A ring of a mean diameter 30 cm and cross sectional area of 15 cm2 is made up of semi – circular sections of cast iron and cast steel. If each joint has an air gap of 0.25 mm. Find amper turns required to produce a flux of 7 x 10 weber in the magnetic circuit. The relative permeability of steel and iron are 852 and 165 respectively. - OA- Amper turns required= 1105 OB- Amper turns required= 1995 OC- Amper turns required= 2250 OD- Amper turns required= 3150 OE- None of above ارسال الاجابةarrow_forwardThe force exerted on the length element dl at point P in the circular conductive ring in the figure, Please choose one: a.It is tangent to the ring on the note P. b.It's inward throughout the OP. C.It is outward throughout the OP. D.It is in the direction of the magnetic field.arrow_forward
- For this problem, please use the figure below. For the magnetic core, the mean length is 50 cm, cross-sectional area is 5 square cm, and relative permeability of the core is (8000/). If the length of the air gap is 0.00525 cm (yes, multiplied by pi) and assuming fringing in the air gap causes the effective cross-sectional area to increase by 5%, determine the total reluctance for this magnetic circuit. Express your answer in ampere-turns per weber, rounded off to the nearest thousand [1,000 A- t/Wb]. Figure for Problem 5 Core: mean length le area A. permeability j Coil: N turns Answer: Air gaparrow_forwardPls quick. I need the final answerarrow_forwardPls quick. I need the final answerarrow_forward
- The loop shown in the figure consists of radial lines and a circular segment centered at point P. Find the magnetic field ?⃗⃗ at point P...arrow_forwardAn iron rod with diameter of 1.5-centimeter was formed into an almost perfect circular ring (including the air gap at the joint) having an average centerline radius of 10.0-centimeter. The air gap is 0.25 centimeter in length. A coil of 200 turns was wounded on the ring and a current of 5.0-amperes DC was made to flow using external DC source. Considering magnetic flux fringes on the air gap , the effective cross sectional area of the air gap increased by 5% compared to that of the rod. Relative Magnetic Permeability of Iron = 5500. Consider the average or centerline circumference of the ring as the total magnetic path (rod+airgap). 1. What is the total Reluctance of the ring ( rod + air gap ) (A-turns/Wb) ? 2.What is the magnetic flux generated in the ring? 3. What is the magnetic flux density in the air gaparrow_forwardA ferromagnetic core with a relative permeability of 1500 is shown in the Figure. The dimensions are shown in the diagram, and the depth of the core is 5cm. The air gaps on the left and right sides of the core are 0.050 and 0.070 cm, respectively. Because of the 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, what are the flux values for the left, center, and right legs of the core? What is the magnetic field in each air gap? |7 cm 7 cm 7 cm to 30 cm 30 cm 7 cm 30 cm 0.07 cm 300 turns 0.05 cm 7 cm Core depth = 5 cmarrow_forward
- 3. A magnetic circuit consists of silicon steel 3000 permeability of 10-cm length and cross section of 1.5 sq.cm and an air gap of the same cross section and of 2 cm length. A ½ ampere current flows through 500 turns. What is the field intensity at the air gap? a. 156.8 Gauss b. 135.6 Gauss c. 140.6 Gauss d. 164.0 Gaussarrow_forwarda conductor moving with a velocity of 5.0 m/s to the right in the presence of a magnetic field. The flux density is 0.5 T into the page, and the wire is 1.0 m in length, oriented as shown. What are the magnitude resulting induced voltage?arrow_forwardFigure shows a circuit and a conducting rod. A conducting rod moves with a constant velocity vperpendicular to a circuit with a current I=2.82sin(??)arrow_forward
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