Answered: Calculate the divergence and Curl, of…

Calculate the divergence and Curl, of the following functions a. V= x2 i+3xy2 j -2xyz k b. V=xyi+2yz j+3zx k c. V= y2i +(2xy+z2)j+ 2yz k , where i , j , k are unit vectors along x, y and z axis

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter25: Gauss’s Law

Section: Chapter Questions

Problem 1PQ: Which word or name has the same symmetry as the letters in the name ZAK? (Explain your answer.) a....

See similar textbooks

Related questions

Q: Given: AB = 1 (AXB dot C) I m BC = 1 (BXC dot A) Im AC = (A dot B) m %3D A = 4it5j+4k m B = 2i+4j+6k…

Q: A student takes a much needed break from her studies and wanders around in the Arnold Arboretum.…

Q: What is the x component of A?

A: From the graph, dx = 3 dy = 3

Q: A particle moves in one-dimensional motion through a field for which the potential energy of the…

A: given quantities: U(x)=(A)/(x3) -B/x A=0.15 B=3.68 (a) To find the equilibrium position , first ,…

Q: Q.8 Find the directional derivative of o = r² + sin y–rz in the direction i+2j– 2k at the point (1,…

Q: m Which of the following correctly expresses the relationsh

Q: 1. Image that two particles, a proton and an electron, are confined to move on circular rings of…

A: Here by conservation of angular momentum we have L=Iw where I is the moment of inertia and w is the…

Q: (c) Prove that F(r, y, 2) = (y² cos r+)i + (2y sin r - 4)j+ (3rz² + 2)k COs is a conservative vector…

A: Given, Force, F→x,y,z = y2 cos x + z3 i^ + 2y sinx -4j^ + 3xz2 + 2k^

Q: A. Determine the fundamental dimensions of Coulomb's constant k. This constant relates the…

Q: It is given as A =i-3j+2k and B =2j-4k. What is the angle between vector A and vector B ?

A: Given A =i-3j+2k B =2j-4k.

Q: (a) What is the dimension of area moment of inertia? (b) If the thickness of a piezoelectric…

Q: Problem 2: The force along rod AC is 1000 N. a) Express the force on rod AC, FAC, as a Cartesian…

A: From the diagram, the coordinate of point A or point C is: The vector along rod AC is:

Q: 11. Determine the magnitude of the projected component of force F. asta along z axis. АВ SOLUTION…

A: Given: Force FAB = 700 lb.

Q: A vector field is given as W = 4x2y ax - (7x + 2y) ay + (4xy + 2x2) az. If the field is at point…

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

A: 1

Q: (a) Find the mass density of a proton, modeling it as a solid sphere of radius 1.00 x 10-15 m. (b)…

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you.…

Q: the general mathematical formula of the potential function in 3-D is V(x,y,z)= mgz-c O V(x,y,z)=…

Q: 02: Determine the magnitude of the force (F) so that the resultant (FR) of the three forces is as…

Q: Find the x- and y-components of E2. E2x = E2 cos 180° = (1.8 × 106 N/C) cos 180° = -1.8 x 106 N/C…

A: A vector which is in 2D has two perpendicular components in the X- and Y-axes. The X- component of a…

Q: In Problems 37 to 40, evaluate the triple integrals. -2x 37. dz dy dx 38. dy da dz 2=0 y=82 -2 2y+%3…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

Q: Evaluate the commutator L,, L, L,- (a) h'L, (b) 0 (c) h'L, (d) h°L.

A: In rotational mechanics, Angular momentum holds a similar place as linear momentum. If Net torque on…

Q: 6.1 Given V -5x'y'z and e 2.25e find (a) E at point P(-3, 1, 2), (b) p, at P. %3D

A: Given: The potential is V=5x3y2z. The the permittivity in a medium is ε=2.25εo. Part (a) The…

Q: 4- if Á = x?i – yj + zk,B = yi + xj - xyzk, q = x?y + zx + yz? , find : (a) Vợ at point (1, –1,2) .…

A: "Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: 1. Show that F is a conservative vector field and then find a function f such that F = Vf where F(x,…

A: We have a vector field which is given by the expression F→=(exlny)i^+(ex/y+sinz)j^+(ycosz)k^. We…

Q: Problem#2: Compute for the moments brought about by F and by P at points A, B, and C given F = 450 N…

Q: a) Define gravitational potential. b) Show that on the earth s surface, the gravitational potential,…

Q: A PN flip-flop has four operations: clear to 0, no change, complement, and set to 1, when inputs P…

A: Given:A PN flip flop has four operations: clear to 0, no change,complement, and set to 1, when…

Q: Consider a triangle ABC with sides AB = 14.9 cm and BC = 9.7 cm. Angle ABC is 38.4 degrees. What is…

Q: What the points of are interection of the two curves r=5 sine , r= 2+Sin 8

A: We'll find the point of intersection by equating the given two equations.

Q: An old model of a hydrogen atom has the charge +e of the proton uniformly distributed over a sphere…

Q: a) What is the speed of the proton if it is not deflected? (that is, it moves in a straight line…

Q: 1. One morning, Connie walks from her house to go to a store that is 500 ft, S 40° W from her house.…

A: Step 1: Note Question (1) is Solved here. For Question (2) , Please Post this question again.

Q: Problem#2: Compute for the moments brought about by F and by P at points A, B, and C given F = 450 N…

Q: 120. A particle of charge -q and mass m is placed at the center of a uniformaly charged ring of…

Q: и (N) 8 4 Review. The graph in Figure P7.20 specifies a functional relationship v (cm) 30 10 20…

A: From the graph, the equation of the line is: Also,

Q: Scientists in the laboratory create a uniform electric field E = 9.0x105 k V/m in a region of space…

Q: C = -3.0î + 4.0j , and and (d) C = -2.0 i +3.0 j +2.0k and Á =-9.0 j . 68. cross product A × Ć for…

Q: Q2)lf a 1.5cm radius, 2V conductor embedded in silica is 10cm far away from a OV conducting plane;A)…

A: Given, Radius r1 = 1.5 cm V1 = 2 V Distance r2 = 10 cm Voltage V2 = 0 V We know the expression…

Q: a1 In the following circuit R,- 10.0 a, R,- 20.0 , R - 4.0 n and Ra - 8.0n. If la 1.5 A, find 1.l,…

A: Given : R1=10Ω, R2=20Ω, R3=4Ω, R4=8ΩCurrent, I2 =1.5 A

Q: e) In terms of where R, m, v, q, and B, determine the change in energy of particle 4 from the time…

A: (e)Magnetic field never does any work, as it's force is always perpendicular to the direction of…

Q: 1. One morning, Connie walks from her house to go to a store that is 500 ft, S 40° W from her house.…

Q: If r is going from the origin to the point (x,y,z) and r#0 I prove the following relations: V«($) -…

Q: Q2: Consider a force F given by p2 + ar + B" where r is the position vector to point (x, y), r is…

A: The force is a vector quantity that is defined as the rate of change of momentum of an object by…

Q: 1) For A = 2î - 3j and B = i+ 2j-k vectors; a) Determine the angle between the vectors A +B and A-B;…

Q: A particle (q = 3.0 µC, m = 10 g) has a speed of 40 m/s when it enters a region where the electric…

Q: Complete the Tables 790 2 2.2 k2 ww R4 ww 8.6 k2 32 V 1 k2 630 2 ww R2 R, R3 R. R, Total V R 790 2 1…

Q: Problem#2: Compute for the moments brought about by F and by P at points A, B, and C given F = 450 N…

Question

Q8. Calculate the divergence and Curl, of the following functions

a. V= x2 i+3xy2 j -2xyz k
b. V=xyi+2yz j+3zx k
c. V= y2i +(2xy+z2)j+ 2yz k , where i , j , k are unit vectors along x, y and z axis

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 Given

VIEW

Step 2 Solution

VIEW

Step 3 Solution

VIEW

Step by step

Solved in 3 steps with 2 images

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

Which word or name has the same symmetry as the letters in the name ZAK? (Explain your answer.) a. NUT b. SUE c. CAL d. BIG
What is the scalar/dot product of the given 3-dimensional vectors: A = (xy)i + (2yz)j + (3xz)k and B = (yz)i + (2xz)j+(3xy)k , if x = 1; y = 2; z = 3? %3D %3D %3D O 144 136 O 132 O 138
Given the function y =3xyz2i + 2xy³j-x2yzk Find the curl Vxu a. 3yz'i + 6xy2j - x²yk b. Зyz? + 6ху?- х2у c. -x*zî + 8xyzj + [2y³ - 3xz²]k d. -x2z + 8xyz+ [2y³ – 3xz²]
7) Calculate the divergence and Curl, of the following functionsa) V= x 2 i +3xy2 j -2xyz kb) V=xy i+2yz j+3zx kc) V= y 2 i +(2xy+z 2 )j+ 2yz k , where i , j , k are unit vectors along x, y and z axis
In Problems 37 to 40, evaluate the triple integrals. -2x 37. dz dy dx 38. dy da dz 2=0 y=82 -2 2y+%3 -2x 1/z 39. 6y dx dz dy 40. z dy dz dr. y=-2 Jz=1 Jx=y+z r=1 Jz=r
The figure shows four vectors A, B, C and D having magnitudes 12.0 m, 10.0 m, 8.0 m, and 4.0 m, respectively. The sum of these four vectors is y B 30° + 30° X D 1076 2 48432 W S mand X M O a. 16.4 m at an angle 77.8° with respect to +X-axis. Ob. 16.4 m at an angle 12.3° with respect to +X-axis. c. 19.5 m at an angle 77.8° with respect to +X-axis O d. 19.5 m at an angle 12.30 with respect to +X-axis. O e. 8.20 m at an angle 77.8° with respect to +x-axis. F2 s # 3 E D 31, C M 80 $ 4 R F a FA % 5 V #tv ♫ T o FS G 6 B c Fo Y H & 7 N F7 p U 8 J DII FB 1 M ( 9 K F9 O A ) O 4 F10 L e e P il V F11 { 11 + [ C F12 command option O
Problem 1 Let A = 3 i - 3j +k and B= -2 i + (-1) j + 5 k. A. What is the cross product C = B x A ? B. What is the dot product C B?
Polnts out of 10.00 P Rag question 5x2 522 Let f(x, y, z) = 5y If the level surface 2 f(x, y, z) = 5 has the surface area element of the form do = B(x, y, z)dædz, then evaluate B(2/5,21,2/5). O A. 7.5574 O B. -8.5826 O C. 6.4031 O D. 5.5678 O E. 4.5826 O F. 3.4031 O G. 6.0828 O H. -4.5826
Evaluate an area of a surface where the vector that is normal to the surface is defined as; a. R = 4yz az for 1
A vector field is defined by: F (x,y,z) = -xi - yj + zk Select the option that gives F expressed in cylindrical coordinates. A. F (r,ø,z) = -reø + zezB. F (r,ø,z) = (-x cos ø - y sin ø) er + (x sin ø - y cos ø) eø + zez C. F (r,ø,z) = - rer + zez D. F (r,ø,z) = reø + zez E. F (r,ø,z) = (x sin ø - y cos ø) er + (-x cos ø - y sin ø) eø + zez
Elliptical cylindrical (EC) coordinates are defined by the variables u, v and z, with aconstant a, in terms of Cartesian coordinates as follows:x = a cosh u cos v ;y = a sinh u sin v ; (75)z = z .a. Find the EC metric.b. Describe surfaces of constant u, v and z for various values of the constant a.c. Find the EC basis vectors for arbitrary a.d. Make vector field plots of the EC basis vectors in the x-y plane.e. Find the incremental area and volume expressions.f. Express the gradient, divergence, curl and Laplacian operators in EC coordinates.
If the plane passing through the points are: A (3, -2, 1), B (-1, 0, 2), and С (4, -3, 4) a. Find the angle of vector AB and AC using cross product and b. Ах В c. unit vector of B