Sketch the vector function
and compute its divergence.
Sketch the vector function: 02 2 1 Compute its divergence. The answer may surprise you...can you explain it?
8. Sketch the vector function: F/r2 and computer its divergence. The answer may surprise you...can you explain it?
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...
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.
(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...
Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in the flux form of Green's Theorem and check for consistency. c. State whether the vector field is source free. F = (8xy,9x2 - 4y?); R is the region bounded by y = x(6 - x) and y=0. .- a. The two-dimensional divergence is 0 b. Set up the integral over the region. dy dx 0 Set...
Consider the following region and the vector field F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency F= (2x-2y); R=(x,y): x2 + y²59 a. The two-dimensional divergence is (Type an exact answer.) b. Set up the integral over the region. Write the integral using polar coordinates with r as the radius and O as the angle SO rdr d0 (Type exact answers.) 0 o Set up the line...
2. a) Verify the divergence theorem for the function in cylindrical coordinates, for a cylinder of radius R and height L with its axis along the z-axis. b) Verify the divergence theorem for the function in spherical coordinates, for the half of a sphere of radius R that extends from φ-0 to φ-T.
(a) Prove that the divergence of a curl is always zero for any vector field. (b) Prove that the curl of the gradient of a scalar function is always zero.