Compute the flux of the vector field F =< r(2 + sin 0), r sin ở cos 8, 3z > through the surface S where S is the surface bounded by r= 2, z = 0, z = 5 in the first octant. Round off answer to 2 decimal places. NOTE: if answer is Spi, write 15.71 O 20pi O Spi O none of these above O 25pl O 30pi

Compute the flux of the vector field F =< r(2 + sin 0), r sin ở cos 8, 3z > through the surface S where S is the surface bounded by r= 2, z = 0, z = 5 in the first octant. Round off answer to 2 decimal places. NOTE: if answer is Spi, write 15.71 O 20pi O Spi O none of these above O 25pl O 30pi

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 26P: A vector field is pointed along the z-axis, v=ax2+y2z . (a) Find the flux of the vector field...

See similar textbooks

Related questions

Q: Find the curl of the vector field F =

Q: Determine the divergence of these vector fields: 1 T cos 8 a, + r sin 0 cos o a, + cos 0 a

Q: 2.2 Express the following points in cylindrical and spherical coordinates: (a) P(1, –4, –3) (b) Q(3,…

Q: Consider a rectangular surface of length L and width W in the xy plane with its center at the…

Q: Let F be the vector field F(r, y, z) = 2²i – sin yj + (2.rz + 622)k. Compute divergence and gradient…

Q: Find the k-component of (curl F) for the following vector field on the plane. F = (xe)i + (8y ex)j…

A: The vector field on the plane is given as F=xeyi^+8yexj^

Q: Given the vector field, G =y Find the following: i. G at Q ii. Scalar component of G at Q in the…

A: To determine: (1) The vector field G at Q for the given vector field Given vector, G=yax-2xay+4az…

Q: Find the flux through the top, left, and right sides of a cube of side 1.75 m when placed in a…

A: The electric flux via the cube’s sides can be represented as, Here, E and A represent the electric…

Q: Find the flux of the vector field F = (y, – z, x) across the part of the plane z = 1+ 3x + 2y above…

Q: z4 k across the surface S the upper hemisphere of x 2 + y 2 +z2 = 9 in the outward direction Find…

Q: Express the vector field W=(x^2-y^2)i +xzk in spherical coordinates at P(4,30degrees,120degrees).

Q: Suppose Vf(x, y) = 6y sin(xy)i + 6x sin(xy)j, F = V f(x, y), and C y = 5x? from the point (1, 5) to…

Q: Q5. a) Find the gradient of the scalar field W = 10rsin²0cosØ . Explain the physical manner of the…

Q: 1. Let F be a vector in Cartesian coordinate system (x, y, z). Determine the divergence of a curl of…

A: 1

Q: Verify if the following vector fields are conservative: a) A₁ (+-) 1 = b) ₂ = (xy, yz, zx) c) A3 =…

A: We have given three vector fields , we need to see whether they are conservative or not. If…

Q: Fompute the curl of the vector field F(r, o,0) = res+ cot o eg

Q: Calculate the areas of the following surfaces using the differential surface area dS p=2,0 ≤z≤ 5,…

Q: Compute the line integral of i = (p cos? 0)p – (p cos e sin 0)ô + 3po, 2 %3D around the path shown…

Q: Calculate the electric flux through the gaussian surface represented by the dashed line, in N m2 / C

A: Given Q1 = -30.2 x 10^{-12} C, Q2 = -9 x 10^{-12 }C, Q3 = 27 x 10^{-12} C, Q4 = 3.9 x 10^{-12} C,…

Q: Two hemispherical surfaces, 1 and 2, of respective radii r1 and r2, are centered at a point charge…

A: The flux can be calculated as follows,

Q: 2. Calculate the total displacement of a cheetah with the following displacement vectors: • Ã = 80…

Q: 4. (20%, ABET-e). Determine the coordinates of the centroid of the area by direct integration.…

Q: Consider the field F(x,y,z)=2y j and the sphere centered at the origin of radius a. We can conclude…

A: This problem can be easily solved by using the law of Gauss's divergence theorem. Which state that…

Q: Find whether the given field vector is: i) conservative, ii) irrotational, iii) both? Justify your…

A: V = yz î + xz j + xy k

Q: Given the function y =3xyz2î + 2xy³j-x2yzk Find the curl Vxu a. 3yz'i + 6xy2j - x²yk b. Зyz? + 6ху?-…

Q: Compute and sketch the vector assigned to the points P (0, 6, –1) and Q = (4, 1,0) by the vector…

A: Given, P =(0, 6, -1)Q = (4, 1, 0)Vector field, F = xy, z2, x

Q: The vector field D* = e*r (cos2q) r3 is defined within the spherical shell whose inner and outer…

Q: Consider a vector field of A = (2x-z) i + xyj - x ²k taken over the region (a cube) bounded be x =…

A: Vectors are physical quantities that have both magnitude and direction. Scalars on the other hand…

Q: Express the uniform vector field F = 5ax in (a) cylindrical components. Please show the STEP-BY-STEP…

Q: Evaluate [[ F · ndS (i.e., find the flux of F across S) where F(x, y, z)=-y, x, z² > and S is the…

A: Given F→ = -yx^ + xy^ + z2k^ x2 + y2 + z2 = 4 as the hemisphere is oriented in the direction of the…

Q: Express the uniform vector field F = 5ax in (a) cylindrical components; (b) spherical components.

A: ^

Q: Get the expression for the divergent of a vector field in spherical coordinates.

A: Given : Divergence : Divergence of a vector field is a measure of the “…

Q: Given a vector field A = 5x ^ 2(sin (pi*x)/2) i, find V.A at x = 1

A: Vector A = 5x².(sin (pi.x)/2)i

Q: ELECTRIC FLUX Write the given and complete solution. 1. A uniform electric field E = 8000 N/C…

A: Part (1): Given: The cross-section area of the plate is 10 m2. The strength of the electric field is…

Q: Let F(r, y, 2) = 3z7- 2y 3 – (x + y) E. For each of the surfaces in Parts (a)-(d), say whether the…

A: Hi. Since you have posted a question with multiple subparts and not specified which subparts you…

Q: The field B = -2ax + 3ay + 4az mT is present in free space. Find the vector force exerted on a…

A: Given, Current, i = 2 A Magnetic field vector, B = −2ax+ 3ay+ 4az mT = B = (−2ax+ 3ay+ 4az)10-3 T…

Q: Find the flux of the vector field F = k through the upper half of the sphere r? + y² + z2 = 4. 4pi…

A: Sphere : x2 + y2 +z2 =4 Radius = 40.5 = 2 units

Q: Let C be the unit circle oriented in the counterclockwise direction. Calculate the outward flux of…

A: Given- F(x,y)=<x3+siny,y3+cosx2>

Q: Find the gradient field F = Vq for the potential function below. P(x,y.z) = In (3x +y° + +z?)…

Q: . Show that the vector field F(x, y) = ( 2xy, x² + 2y) is conservative. Then, find the potential…

Q: Please answer and write correctly and neatly. A certain vector field is given as G = (y + 1)ax +…

Q: 4. Find the gradient of the following scalar fields: (a) U = 4xz + 3yz (b) W = 2 p (z + 1) cos

Q: A vector field is given by F = y'e*i - x*yj - xtan-'yk use the divergence (Gauss") theorem, to…

A: Given:- F→ = y3ezi^ -x2y j^ -xtan-1y k^

Q: . If a vector field A(x,y,z)=xz'ex - 2x°yzey+2yz´ez , calculate the curl 7xA at point M(1,-1,-1).

A: In vector calculus, the curl of a vector field is a quantity that describes the infinitesimal…

Q: ) Show that the curl of (b x7) is 2b. Where i is the position vector

Q: Given a vector field D = 2xy² ax + x² av and the rectangular parallel pipe formed by the planes x =…

A: Given: The vector field , Here , x , y, z are the planes of a rectangular parallel pipe. The flux…

Q: For each of the following vector fields F , decide whether it is conservative or not by computing…

Concept explainers

Debye Theory of Solids

In solid-state physics, debye theory is used to estimate the phonons contributing to the specific heat capacity in a solid. It explains that the specific heat is a consequence of the vibrations of the atomic lattice of the solid, which is in contrast to the Einstein model. In the Einstein model, solids are treated as independent, non-interacting quantum harmonic oscillators. This model clearly explains the low-temperature dependence of the heat capacity, which is proportional to T3. This is known as Debye T3 law.

Question

COMPUTE THE FLUX

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 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, physics and related others by exploring similar questions and additional content below.

Similar questions

+Y ↑ +X In figure-1, the coordinate of charge g = 17 µAs R (4,4), the coordinate of charge = 12 uAs P (11, 4) and the coordinate of charge 9 = 15 µas P (11,9) The coordinates have centimeters as unit. a Find the vector pointing from g to 2. This vector is denoted by 712- rcomponent of 12 Give your answer to at least three significance digits. ст y component of 12 Give your answer to at least three significance digits. bFind the unit vector 12. rcomponent of Ê12 Give your answer to at least three significance digits. cm y component of 12 Give your answer to at least three significance digits. cm Submit
Compute the flux of F through the cylindrical surface S centered on the z-axis, oriented away from the z-axis. F(x, y, z) = 3y7 + 2xzk S: radius 4. x ≥ 0, y ≥ 0,0 ≤ ≤ 2 Enter an exact answer. S . dA = i 640
es Given the general vector field A = 10 sind ae in spherical coordinates, find the VXA at (2, π/2, 0).
Consider a vector field of A = (2x-z) i + x²yj - x zk taken over the region (a cube) bounded be x = 0, x=1, y=0, y = 1, z = 0, and z = 1. Evaluate a) ſ div A dV b) SA. dS
7. For the vector field K = x²yi+ xz³ j– y²z²k, evaluate a. curl K b. grad div K
de The value of the integral I = 2+cos e 2n O TI V3
Three charged patides ar ocated at the comers of an equitateral triangle an shown in the figurn below (let a3.00 C, and 910 m). Calculate the total electric force on the 7,00-pc chargn. maituteA X N dron XCtercucwie from the
Express the vector field W = (x² – y²)a, + xza, in the (a) Cylinderical coordinate at P(p = 6, q = 60, z = -4). (b) Spherical coordinate at P(r = 4, 0 = 30, p = 120). %3D
guidelines: Answers must be expressed in engineering notation (when the exponent of the base 10 multiplier is not a multiple of 3, press ENG or SHIFT+ENG, whichever the case.) Example: 0.06N or 6.0x102 N must be expressed to 60x103 N or 60mN A spherical conductor is known to have a radius and a total charge of 10 cm and 20uC. If points A and Bare 15 cm and 5 cm from the center of the conductor, respectively. If a test charge, q = 25mC, is to be moved from A to B, determine the following: a. The potential at A; b. The electric potential energy at B; c. The work done in moving the test charge; d. The rate of change of the potential with respectto length ordisplacement in the conductor
Given that Q=8.4 μC, find the electric flux passing through surface S4. Round off the answer to 2 decimal places and write in the form of scientific representation (nx10m)
A circular area S is concentric with the origin, has radius a, and lies in the yz-plane. Calculate s E ndA for E=2z2i.
A total charge Q is distributed uniformly throughout a spherical volume that is centered at o1 and has a radius R. Without disturbing the charge remaining charge is removed from the spherical volume that is centered at o2 (see below). Show that the electric field everywhere in the empty region is given by E=Qr40R3 where r is the displacement vector directed from o1 to o2 .