Consider the following vector ﬁeld. F = (xi + yj + zk )/((x^2 + y^2 + z^2)^3/2)
(a) Find the divergence of F.
(b) Let S be any sphere not containing the origin. Find the outward ﬂux of F across S.
(c) Let Sa be the sphere of radius a centered at the origin. Find the outward ﬂux of F across Sa.
Consider the following vector ﬁeld. F = (xi + yj + zk )/((x^2 + y^2 + z^2)^3/2) (a) Find the divergence of F. (b) Let S...
can you solve this vector problems? Find the outward flux of the vector field F(x, y, z) = (xi + yj + zk)/(x 2 + y 2 + z 2 ) 3/2 across the ellipsoid 4x^2 + 9y^2 + z^2 = 1. 6. (12 pts.) Find the outward flux of the vector field F(r,y, ) (ri yj+ zk)/(x2 + y2 22)3/2 across the ellipsoid 4r2 +9y2 + z2 = 1 6. (12 pts.) Find the outward flux of the vector...
9. Let Q be the solid bounded by the cylinder x2 + y2 = 1 and the planes z = 0 and z = 1 . Use the Divergence Theorem to calculate | | F . N dS where s is the surface of Q and F(x, y, z) = xi + yj + zk. (a) 67T (d) 0 (b) 1 (e) None of these (c) 3π 9. Let Q be the solid bounded by the cylinder x2 + y2...
(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...
Let F 9xi + yj + zk . S is the part of the surface z = -4x - 2y + 12 in the first octant oriented upward. ey 4,2,1 Find dA X * хр / Set up the iterated integral for flux 3 6 2x F.dA dy dx Let F 9xi + yj + zk . S is the part of the surface z = -4x - 2y + 12 in the first octant oriented upward. ey 4,2,1 Find...
F = r/|r|, where r = xi +yj +zk; S is the sphere ρ = 2 of radius 2 centered at the origin.Use the divergence theorem to evaluate the integral of (F dot n) dS, where n is the outer unit normal vector to the surface S.Please explain your steps thoroughly. I don't understand how to use the S parameters to evaluate.
How do I find the curl and divergence of the vector field F(x,y,z) = {1/√(x2+y2+z2)}*(xi +yj+zk) ?
#4 please 3. (12 pts). (a) (8 pts) Directly compute the flux Ф of the vector field F-(x + y)1+ yj + zk over the closed surface S given by z 36-x2-y2 and z - 0. Keep in mind that N is the outward normal to the surface. Do not use the Divergence Theorem. Hint: Don't forget the bottom! (b) (4 pts) Sketch the surface. ts). Use the Divergence Theorem to compute the flux Ф of Problem 3. Hint: The...
S: y = 0, y = a, z x=0, x = a, 0.2 = a 14. F(x, y, z) = 4xzi + yjt 4xyk 2 15. F(x, y, z) = z21 + yj + zk S: y = 0, y = a, z x=0, x = a, 0.2 = a 14. F(x, y, z) = 4xzi + yjt 4xyk 2 15. F(x, y, z) = z21 + yj + zk
Find the outward flux of F(x,y,z)=(x+y+z)^(-3/2)*(xi+yj+zk) through the ellipse 4x^2+9y^2+z^2=36Thanks a lot ! I am really confused with it.
(1 point) Compute the flux of F xi + yj + zk over the quarter cylinder S given by x2 + y2 -1, 0 3x s 1,0 <y<1,0 3z< 1, oriented outward flux = (1 point) Compute the flux of F xi + yj + zk over the quarter cylinder S given by x2 + y2 -1, 0 3x s 1,0
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