Sketch the vector function: 02 2 1 Compute its divergence. The answer may surprise you...can you...
8. Sketch the vector function: F/r2 and computer its divergence. The answer may surprise you...can you explain it?
Sketch the vector function and compute its divergence. 2
riffiths (Introduction to Electrodynamics (4th edition)): p. 18: Problem 1.16 Sketch the vector function and compute its divergence. The answer may surprise you...can yo
10. Use the Divergence Theorem to compute the net outward flux of the vector field F= <x^2, -y^2, z^2> across the boundary of the region D, where D is the region in the first octant between the planes z= 9-x-y and z= 6-x-y. The net outward flux is __. 11. Decide which integral of the Divergence Theorem to use and compute the outward flux of the vector field F= <-7yz,2,-9xy> across the surface S, where S is the boundary of...
(1) Let G(,y, z) = (x,y, z). Show that there exists no vector field A : R3 -> R3 such that curl(A) Hint: compute its divergence G. (2) Let H R3 -> R3 be given as H(x,y, z) = (1,2,3). Find a vector potential A : R3 -> R3 such that curl(A) smooth function = H. Show that if A is a vector potential for H, then so is A+ Vf, for any f : R5 -> R (3) Let...
Use the Divergence Theorem to compute the ux of the vector eld F(x, y, z) = .5x^2i-(1/3)y^3zj+1/2y^2z^2k through the boundary of the cylinder determined by x2 + y 2 ≤ 4, 0 ≤z ≤ 2.
show work please Written Homework 10, Due May 2 Name 3. (11 point) (a) (5 points) Find the projection of the vector (3,4) onto the vector (0,6). Sketch a picture of these vectors and its projection vector. (b) (6 points) Find a vector parallel to the vector (3,4) whose projection onto the vector (06) is equal to (0.2). Page 3 Written Homework 10, Due May 2 Name 3. (11 point) (a) (5 points) Find the projection of the vector (3,4)...
Help would be greatly appreciated!! 1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this...
Q1) Sketch the following vector fields, showing vector at whole number coordinates be- tween -2 and 2. Q2) Consider the curves C1 and C2 plotted against the vector field below. What are the signs of the path integrals JG F. d? Explain your answer 2/ Q1) Sketch the following vector fields, showing vector at whole number coordinates be- tween -2 and 2. Q2) Consider the curves C1 and C2 plotted against the vector field below. What are the signs of...
B.2. The surface Sc of an ice-cream cone can be parametrised in spherical polar coordinates (r, 0, 0) by where θ0 is a constant (which you may assume is less than π/2) (a) Sketch the surface Sc (b) Using the expression show that the vector element of area on Sc is given by -T Sin where [41 (c) The vector field a(r) is given in Cartesian coordinates by Show that on Sc and hence that 4 2 (d) The curved...