Einstein notation.Curl of the rotation field. For the general rotation field F=axr, where a is a non zero vector and r=<x,y,z>. Show that curl F=2a with Einstein notation
Einstein notation.Curl of the rotation field. For the general rotation field F=axr, where a is a...
you can skip #2 Show that F() = Vf (), 1. Let F R3 -R be defined by F(I) = F12", where u where f(r,y,) = =- +22 2. Consider the vector field F(E,) = (a,y) Compute the flow lines for this vector field. 3. Compute the divergence and curl of the following vector field: F(x,y,)(+ yz, ryz, ry + 2) Show that F() = Vf (), 1. Let F R3 -R be defined by F(I) = F12", where u...
Consider the vector field (-7.-2.3) xr, where r= = (x,y,z). a. Compute the curl of the field and verify that it has the same direction as the axis of rotation b. Compute the magnitude of the curl of the field. a. The curl of the field is (i+O; Ok b. The magnitude of the curl of the field is (Type an exact answer, using radicals as needed.)
Find the curl of the vector. Find the curl of the following vector field: t-y where b is a constant and r = x-+y +z
(1) Let F denote the inverse square vector field (axr, y, z) F= (Note that ||F 1/r2.) The domain of F is R3\{(0, 0, 0)} where r = the chain rule (a) Verify that Hint: first show that then use (b) Show that div(F 0. (c) Suppose that S is a closed surface in R3 that does not enclose the origin. Show that the flux of F through S is zero. Hint: since the interior of S does not contain...
Let F 10i4u 8zk. Compute the civergence and curl of F. , div F , curl F Show steps (1 point) Let F (8y2)i(7xz)j+(6y) k Compute the following: A div F В. curl F- i+ k C, div curt F= Note: Your answers should be expressions of x, y and/or z; e.g. "3xy" or "z" or 5 (1 polnt) Consider the vector field F(r,y, ) = ( 9y , 0, -3ry) Find the divergence and curl of F div(F) VF=...
Consider the vector field. F(x, y, z) = 6ex sin(y), 8ey sin(z), 5ez sin(x) Consider the vector field. F(x, y, z) = (6e* sin(y), 8ey sin(z), 5e? sin(x)) (a) Find the curl of the vector field. curl F = (-8e'sin(z), – 5e'sin(x), – 6e'sin(y)) x (b) Find the divergence of the vector field. div F = 6e sin(y) + 8e) sin(z) + 5e+sin(x)
Consider the vector field. F(x, y, z) = (98 sin(y), 4e' sin(z), 2e sin(x)) (a) Find the curl of the vector field. curl F = (b) Find the divergence of the vector field. div F =
ems (1 point) A) Consider the vector field F(x, y, z) = (6yz, -7zz, zy). Find the divergence and curl of F. div(F) = V.F= curl(F) = V F =( ). 5 (5x?, 2(x + y), -7(x + y + x)) 7 B) Consider the vector field F(x, y, z) Find the divergence and curl of F. div(F) = V.P= curl(F) = V XF =( 8 9 10 )
Consider the vector field. F(x, y, z) = (3ex sin(y), 3ey sin(z), 5e7 sin(x)) (a) Find the curl of the vector field. curl F = (-3d"cos(z))i – (36*cos(x)); – (5e+cos(y) )* * (b) Find the divergence of the vector field. div F = 3e'sin(y) + 3e'sin(z) + 5e+ sin(x)
(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...