EBK FUNDAMENTALS OF APPLIED ELECTROMAGN
7th Edition
ISBN: 8220100663659
Author: ULABY
Publisher: PEARSON
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Chapter 3, Problem 43P
To determine
The directional derivative of
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Calculate the current magnitude in the coils e1, e2 of theMagnetic circuit, if:ɸa = 3.00 x 10^-3 Wb, φb = 0.80 x 10^-3 Wb, ɸc = 2.20 x 10^-3 Wb
L ab = 0.10 m,A ab = 5.0 cm^2L afeb = L acdb = 0.40 mA afeb = A acdb = 20 cm^2
MATERIAL CHARACTERISTICSH (At/m) 240 350 530 1300 5000 9000B (T) 0.7 0.9 1.1 1.3 1.5 1.6
A toroid magnetic circuit is composed of three sections A, B and C, thesection C has an air gap, section A has an 850 round coil thatconsumes a current of 1.2 A. the physical and magnetic properties of each sectionare:
Section A: Length = 80 mm, Cross section = 120 mm^2, μr = 400
Section B: Length = 60 mm, Cross section = 40 mm^2, μr = 250
Section C: Length = 50 mm, Cross section = 200 mm^2, μr = 600
Gap: Length = 1 mm, Cross section = 40 mm^2, μr = 1
Calculate:The magnetic field density in each of the sections
3) Compute the input impedance of Fig. 3. (10 points)
Rin
R1
R₂
Figure 3
T
Vcc
Chapter 3 Solutions
EBK FUNDAMENTALS OF APPLIED ELECTROMAGN
Ch. 3.1 - When are two vectors equal and when are they...Ch. 3.1 - Prob. 2CQCh. 3.1 - If AB = 0, what is AB?Ch. 3.1 - If AB = 0, what is AB?Ch. 3.1 - Is A(BC) a vector triple product?Ch. 3.1 - If AB = AC, does it follow that B = C?Ch. 3.1 - Find the distance vector between P1 = (1, 2, 3)...Ch. 3.1 - Find the angle AB between vectors A and B of...Ch. 3.1 - Prob. 3ECh. 3.1 - Vectors A and B lie in the y-z plane and both have...
Ch. 3.1 - If AB=AC, does it follow that B = C?Ch. 3.2 - A circular cylinder of radius r = 5 cm is...Ch. 3.3 - Why do we use more than one coordinate system?Ch. 3.3 - Prob. 8CQCh. 3.3 - Prob. 9CQCh. 3.3 - How is the position vector of a point in...Ch. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Find the directional derivative of V=rz2cos2 along...Ch. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.5 - Given A=e2y(xsin2x+ycos2x), find A.Ch. 3.5 - Given A=rrcos+rsin+z3z , find A at (2,0, 3).Ch. 3.5 - If E=RAR in spherical coordinates, calculate the...Ch. 3.5 - Verify the divergence theorem by calculating the...Ch. 3.5 - Prob. 17ECh. 3.6 - Find A at (2, 0, 3) in cylindrical coordinates for...Ch. 3.6 - Find A at (3, /6, 0) in spherical coordinates for...Ch. 3.7 - What do the magnitude and direction of the...Ch. 3.7 - Prob. 12CQCh. 3.7 - Prob. 13CQCh. 3.7 - Prob. 14CQCh. 3.7 - What is the meaning of the transformation provided...Ch. 3.7 - Prob. 16CQCh. 3.7 - Prob. 17CQCh. 3.7 - When is a vector field conservative?Ch. 3 - Prob. 1PCh. 3 - Given vectors A=x2y3+z, B=x2y+z3, and C=x4+y2+z2,...Ch. 3 - Prob. 3PCh. 3 - Prob. 4PCh. 3 - Given vectors A=x+y2z3, B=x2y4, and C=y2z4, find...Ch. 3 - Given vectors A=x2y+z3 and B=x3z2, find a vector C...Ch. 3 - Given A=x(x+2y)y(y+3z)+z(3xy), determine a unit...Ch. 3 - By expansion in Cartesian coordinates, prove: (a)...Ch. 3 - Find an expression for the unit vector directed...Ch. 3 - Prob. 10PCh. 3 - Prob. 11PCh. 3 - Prob. 12PCh. 3 - A given line is described by x+2y=4. Vector A...Ch. 3 - Prob. 14PCh. 3 - Prob. 15PCh. 3 - Given B=x(z3y)+y(2x3z)z(x+y), find a unit vector...Ch. 3 - Find a vector G whose magnitude is 4 and whose...Ch. 3 - A given line is described by the equation: y=x1....Ch. 3 - Vector field E is given by E=R5Rcos12Rsincos+3sin....Ch. 3 - Prob. 20PCh. 3 - Prob. 21PCh. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Use the appropriate expression for the...Ch. 3 - Prob. 26PCh. 3 - A section of a sphere is described by 0 R 2, 0 ...Ch. 3 - A vector field is given in cylindrical coordinates...Ch. 3 - At a given point in space, vectors A and B are...Ch. 3 - Given vectors...Ch. 3 - Prob. 31PCh. 3 - Prob. 32PCh. 3 - Transform the vector A=Rsin2cos+cos2sin into...Ch. 3 - Transform the following vectors into cylindrical...Ch. 3 - Transform the following vectors into spherical...Ch. 3 - Find the gradient of the following scalar...Ch. 3 - For each of the following scalar fields, obtain an...Ch. 3 - The gradient of a scalar function T is given by...Ch. 3 - Prob. 39PCh. 3 - For the scalar function V = xy2 z2, determine its...Ch. 3 - Evaluate the line integral of E=xxyy along the...Ch. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - Each of the following vector fields is displayed...Ch. 3 - Prob. 45PCh. 3 - For the vector field E=xxzyyz2zxy, verify the...Ch. 3 - For the vector field E=r10erz3z, verify the...Ch. 3 - A vector field D=rr3 exists in the region between...Ch. 3 - For the vector field D=R3R2, evaluate both sides...Ch. 3 - For the vector field E=xxyy(x2+2y2), calculate (a)...Ch. 3 - Repeat Problem 3.50 for the contour shown in Fig....Ch. 3 - Verify Stokess theorem for the vector field...Ch. 3 - Prob. 53PCh. 3 - Prob. 54PCh. 3 - Verify Stokess theorem for the vector field B = (r...Ch. 3 - Prob. 56PCh. 3 - Prob. 57PCh. 3 - Find the Laplacian of the following scalar...
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