A cube is defined by 1 < x, y, z < 1.2. If D = 2x²ya, +3x²y²a, C/m². (a) Apply Gauss's law to find the total flux leaving the closed surface of the cube. (b) Evaluate V · D at the center of the cube. (c) Estimate the total charge enclosed within the cube by using Eq. (8).

A cube is defined by 1 < x, y, z < 1.2. If D = 2x²ya, +3x²y²a, C/m². (a) Apply Gauss's law to find the total flux leaving the closed surface of the cube. (b) Evaluate V · D at the center of the cube. (c) Estimate the total charge enclosed within the cube by using Eq. (8).

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Related questions

Q: QUESTION 3 (a) Given the electric field in free space as 2x(1 + z*) E 4xz a, +- -az. Find the amount…

A: a) Given plane is z=1. Electric field is E¯=2x(1+z2)ε0ax+4xzε0az The amount of electric flux…

Q: D4. ( In free space, two spherical surfaces at r = 1 and r 2 carrying surface charge densities…

Q: HW: A spherical charge of (pv= 6 C/m3 ) and radius ( 4). Its center is at (1,2,3). Find settings(E)…

A: Given data, ρv=6 Cm3r= 4 m Now, r'=1-32+2--22+3-42=21 The formula of E is The electric field…

Q: H.W 2. Line charge of charge density of PL C/m lying along z-axis in free-space from -L to L,…

A: Electric field due to finite line charge density

Q: 3.10.[1] A cube is defined by 1 < x, y, z < 1.2. If D = 2x²y a, + 3x²y² a, C/m²: (a) apply Gauss's…

A: Given:-1<x,y,z<1.2D=2x2yax+3x2y2ay

Q: D3.6. In free space, let D = 8xyz'a, + 4x*z*a,y + 16x yz'a, pC/m?, (a) Find the total electric flux…

A: Given data: D=8xyz4ax+4x2z4ay+16x2yz3az pC/m2 Rectangular surface range, z=2, 0<x<2,…

Q: T:TO_BLU. Q4. The y-axis of the region defined by x=cos(a) and y=sin(2a) in the [-0.5n,0.5n] range…

Q: Infinite uniform line charges of 5 nC/m lie along the (positive and negative) x and y axes in free…

A: The formula of the electric field at a distance L by infinite uniform line charge using Gauss law,…

Q: Problem 4: A point charge Q =D0.4 nC is located at (2, 3, 3) m in Cartesian coordinates. Find the…

A: In this question we will find potential difference due to point charge...

Q: Q2) Evaluate both sides of the divergence theorem to find the total enclosed charge in a spherical…

Q: H.W. 9: Spherical surfaces at r = 2, 4, and 6 m carry uniform surface charge densities of 20 nC/m²,…

A: The spherical spheres at r=2,4and 6 carry a uniform surface charge density is shown below:…

Q: Within the sphere defined by r ≤ 8 cm, the volume charge density is ρv = 6.8 x 10-7 C/m3 . (i) Find…

Q: Q2. Let V = (cos 20)/p in free space. a) Find the volume charge density at point A(0.5, 60º, 1),…

A: a) Calculate the value of . From Poisson’s equation Calculate the value of at point . Thus, the…

Q: D3.6. In free space, let D = 8xyz*a, +4x²z*a,+16x²yza; pC/m². (a) Find the total electric flux…

A: Given D=8xyz4ax+4x2z4ay+16x2yz3az pC/m2 Rectangular surface range, z=2, 0<x<2, 1<y<3

Q: Question 3 A quarter-disc in the first quadrant has a surface charge density given by K cos o C/m2.…

A: Given: A quarter disc in the first quadrant. Surface charge density, σ=Kcosϕ C/m2 Radius, r=b Point…

Q: Q3/Given the current density J = 60 pa, A/m? in cylindrical coordinates: (a) Determine the magnetic…

Q: An infinitely long insulating cylinder of radius R has a volume charge density that varies with the…

A: The given volume charge density is: ρ=ρ0a-rb From the Gauss law, it can be written as:…

Q: * * 5.29 A thin current element extending between z = -L/4 and z = L/4 carries a current I along +î…

Q: Quiz_1) Four point charges Q, 2Q, -Q, -2Q are located at (0,0,a), (0,0,2a), (0,0,-a), and (0,0,-2a)…

A: Take a point charge in the co-ordinate axis (x,y,z) The reference point charge are on the X - axis…

Q: An infinitely long uniform line charge is located at y = 3, z = 5 if ρL = 30nC/m, find E at: (a) the…

Q: Q1: Find the volume charge density in the entire region ( 0 <r < ∞) where the radial electric field…

A: We know that:∇·D=1h1h2h3∂∂rh2h3fh1=1h2=rh3=rsinθD=∈0E

Q: Two uniform line charges, 8 nC/m each, are located at y = 2, z = -1, and at x = -3, z = 2, in free…

Q: Question 2 A circular disk of radius a is uniformly charged with ps C/m2 plane with its axis along…

A: Given radius r=a charge density=ρs C/m2

Q: PROBLEM 2 Calculate the electric field intensity at M (3, -4, 2) in free space caused by a) charge…

A: We will use formula of electric field intensity due to point charge to find out electric field…

Q: (i) Show that the electric field intensity, E at (0, 0, h) in cylindrical coordinates due to…

Q: A sheet of charge , ρs = 2nC/m2 is present at the plane x =3 infree space, and a line charge , ρL =…

Q: PROBLEM 2 Calculate the electric field intensity at M (3, -4, 2) in free space caused by a) charge…

A: We know direct formula for electric field at a particular point due to point charge .

Q: 2. In free space, let D = 8xyz*dx + 6x²z*ãy + 16x?yz*d, pC/m². a. Find the total electric flux…

A: The vector is given by D=8xyz4ax¯+6x2z4ay¯+16x2yz3az¯ pC/m2 a. The electric field is E=Dεo Hence,…

Q: 5.38 A solenoid with a length of 20 cm and a radius of 5 cm consists of 400 turns and carries a…

A: The magnitude of H is plotted as shown below

Q: 2. In free space, let D = 8xyz*ā, + 6x²z*ā, + 16x²yz*ā, pC/m². a. Find the total electric flux…

Q: LaTeX: R = 2mR = 2m radius is uniformly distributed over the sphere volume. Accordingly, which of…

A: Charge 5uC and R = 2m radius is uniformly distributed over the sphere volume. which of the following…

Q: (a) The electric field intensity E =a, -a, exists in the region of free space that includes a…

Q: Q3) In free space, calculate the total electric flux leaving the cylinderical surface defined by:…

A: We need to find out flux leaving the surface due to given charge distribution .

Q: Electric Flux Density, Gauss's law, and Divergence Q2) Evaluate both sides of the divergence theorem…

Q: A charge QA= -20 μc is located at A (-6, 4, 7), and a charge QB= 50 µc is located at B (5, 8, -2) in…

Q: 5.38 A solenoid with a length of 20 cm and a radius of 5 cm consists of 400 turns and carries a…

Q: 8.2 A point charge of 12 nC is located at the origin. Four uniform line charges are located in the x…

A: D is calculated using the following data

Q: Let D = (8x + 4x)ax - 2yay + 2zā, C/m² , use Gauss's Law to determine the charge enclosed in the…

Q: A circular disk of radius a is uniformly charged with ps C/m² . If the disk lies on the = 0 plane…

A: We can assume this charge distribution as a collection of concentration rings of charge.…

Q: Q (6): Two homogeneous dielectrics meet on plane z 0. For z2 0, e-3 and for z0, E=2. A uniform…

A: Homogeneous dielectric A dielectric constant that is not a function of coordinates is called a…

Q: In free space, let D = 8xyz*a, + 6x°z*ãy + 16x?yz a, pC/m². a. Find the total electric flux passing…

A: Given In free space, let D = 8 x y z ax+4x z ay+ 16x²y z³a-pc/m². (a). Find the total electric flux…

Q: 3. Region 1 (z 0) is characterized by &r2 = 4. Let E, = -30a, + 50a, + 70a, V/m, find: а) Е2. b) D2…

A: Given

Q: Given the electric field E= 9ra, -6ya, V/m. find the work done in moving a point charge Q = +2C from…

A: We need to find out the work done for given electric field

Q: Drill 2.5 [1] Two infinite uniform line charges of 5 nC/m charge density lie along x and y axis in…

A: Electric field intensity

Q: Q (6): Two homogeneous dielectrics meet on plane z 0. For z2 0, en 3 and for z 0, E2 2. A uniform…

Q: PRACTICE EXERCISE 8.8 Region 1, described by 3x + 4y 10, is free space, whereas region 2, described…

A: We will use boundary conditions to find B2 . Normal component magnetic flux density is same at the…

Q: D3.6. In free space, let D = 8xyz*a, +4x²z*a,+16x²yz³a, pC/m². (a he total electric flux passing…

A: The solution can be achieved as follows.

Q: A circular disk of radius a [m] is uniformly charged with ps [c/m²]. If the disk lies on the z = 0…

A: Given,Radius of the disk =rmUniform charge = ρs c/m2The disk lies on z=0 plane.

Question

3.17 A cube is defined by 1 < x, y, z < 1.2. If D = 2x²ya, + 3x²y²a,. C/m².
(a) Apply Gauss's law to find the total flux leaving the closed surface of the
cube. (b) Evaluate V. D at the center of the cube. (c) Estimate the total
charge enclosed within the cube by using Eq. (8).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Similar questions

2. A point C is in the Cartesian coordinate system at (2, −3, 6). On location B (−2, 3, −6) has a charge of QB of 55 mC. b) Calculate the electric flux density at point C, which is DC, produced by charge QB.
Example 2.24) In the two-layer uniformly varying field electrode system separated by the X=0 plane, the amplitude of the electric field vector in the first layer is 80kV/cm and the angle it makes with the perpendicular component is 〖20〗^0. Since the relative electric constants of the layers are 4 and 2, respectively, calculate the tangential component of the electric field in the second layer.
In a spherical electrode system, gas material with the most favorable arrangement in terms of puncture resistance, outer radius r2 = 3.2 cm, puncture field strength Ed=75kV/cm and dielectric constant Ergas=1 is used. According to this;a) Calculate the inner radius of the electrode and the puncture voltage of the system according to the geometrical characteristics of the most suitable arrangement in terms of puncture resistance.b) Draw the puncture curve in the p-Emax plane for a voltage of U=40kV provided the outer radius is kept constant and indicate the boundaries of the inner sphere radii on the curve.c) Briefly interpret the electrode system in terms of discharge events in the geometric characteristics of p=0.8, p=1.8 and p=5 on the puncture curve.
A sheet of charge , ρs = 2nC/m2 is present at the plane x =3 infree space, and a line charge , ρL = 20nC is located at x=1, z=4.Find the magnitude of the E at the origin. Complete solution.
9. Given D = 5x2 ax + 10z az C/m2, find the net outward flux crossing the surface of a cube 2m on edge centered at the origin. The edges of the cube are parallel to the edges.
Electromagnetic question Consider a hollow cylindrical surface centered on the z-axis with radius r = a, carrying a uniform surface current density Jsa = 5 af A/m. Additionally, there is a second cylindrical surface with radius r = b (b > a), which carries a current density Jsb = 4 az A/m. Calculate the magnetic field intensity H(r) for the following regions: 1. For 0 < r < a: Determine H(r) using the given parameters. 2. For a < r < b: Calculate H(r) using the given parameters. 3. For r > b: Find H(r) using the given parameters.
A wedge-shaped surface has its corners located at (0, 0, 0), (2, 0, 4), and (2, 3, 4). If thesurface has charge distribution with ρs = 10x2yz mC/m2, find the total charge on thesurface.
Let D = 6xy ax + 2(xz + 3z2) ay + 3yz az C/m2. Evaluate the surface integrals to find the total charge enclosed in the rectangular parallelepiped 0 < x < 2, 0 < y < 2, 0 < z < 4.
SHOW YOUR COMPLETE SOLUTION, MAKE SURE YOUR ANSWERS ARE IN 4 DECIMAL PLACES. A uniform line charge ρL = 15 nC/m lies on the line, x = -6, z = 8, in freespace. Find E in the Cartesian components at:(a) origin
In empty space (er = 1), the region x1 <x <x2 is filled with material with a dielectric coefficient er = 8 as a planar infinitely large plate. The geometry is shown in the figure below. Pay attention to the coordinate system placement.Region I: In (x <x1), the electric field vector was observed as E1 =(4.5) ux + (7.5) uy+(8.5) uz.Region II : (x1 <x <x2) de er = 8 by determining the electric field E2,Write the value of the x-component: E2x numerically.
In empty space (er = 1), the region x1 <x <x2 is filled with material with a dielectric coefficient er = 8 as a planar infinitely large plate. The geometry is shown in the figure below. Pay attention to the coordinate system placement.Region I: In (x <x1), the electric field vector was observed as E1 =(4.5) ux + (7.5) uy+(8.5) uz.Region II : (x1 <x <x2) de er = 8 by determining the electric field E2, write the value of the x-component: E2x numerically
Determine the volume charge density, in pC/m3, at (9, -3, 8) if the electric field present in the region is E = sin (3 x + 2 y + 2 z)(ax + ay + az) V/m. All coordinates are measured in meters.