1. Find the divergence, curl and Laplacian of the following vector fields (a) E = psin...
Please show all workings out many thanks. :) (c)Calculate curl of the vector field E in spherical coordinate where E_ 2 r sin θ ŕ+r2 sin φ@+ r2 sin θώ 5 Marks] (d) Calculate Laplacian of the scaler field f(p, φ, z) in the cylindrical coordinate system, here 5 Marks]
7. Find (a) the curl and (b) the divergence of the vector field F(x, y, z)= e' sin yi+e' cos yj+zk F.de where is the curve of intersection of the plane : = 5 - x and the cylinder rº + y2 = 9. 8. Use Stokes Theorem to evaluate F(x, y, - ) = xyi +2=j+3yk
MARK WHICH OF THE FOLLOWING ARE TRUE/FALSE A. The component of flux, given flux density F, crossing the surface dsu F.ûdsu OB. In spherical coordinates the following is true for any point, r= Rsin o cos 6î + Rsin o sin oſ + R cos and de =R c. The gradient in the u, v, w coordinates is 1 0 1 0 V= ü+T V .hu du h, du + 1 0 hw dw Then, the component of flux, given...
How do I find the curl and divergence of the vector field F(x,y,z) = {1/√(x2+y2+z2)}*(xi +yj+zk) ?
(1 point) Compute the flux of the vector field F 3z2y2 zk through the surface S which is the cone vz2 y2 z, with 0z R, oriented downward. (a) Parameterize the cone using cylindrical coordinates (write 0 as theta). (r,)cos(theta) (r, e)rsin(theta) witho KTR and 0 (b) With this parameterization, what is dA? dA = | <0,0,(m5/2)sin^2(theta» (c) Find the flux of F through S flux
MARK WHICH STATEMENTS BELOW ARE TRUE, USING THE FOLLOWING, Consider Vf(x, y, z) in terms of a new coordinate system, x= x(u, v, w), y=y(u, v, w), z=z(u, v, w). Let r(s) = x(s) i+y(s) + z(s) k be the position vector defining some continuous path as a function of the arc length. Similarly for the other partial derivatives in v and w. For spherical coordinates the following must also be true for any points, x = Rsin o cose,...
Find the divergence and curl of the vector field \(\vec{F}=2 \cos \phi \hat{s}+\frac{z}{s} \hat{z}\)
Find the divergence and curl of the vector field \(\vec{F}=5sin\theta\hat{r}\)
Find the divergence and curl of the vector field \(\vec{F}=y^{2} z^{3} \hat{x}+x y \hat{y}+\left(5 z^{2}+y\right) \hat{z}\)
Calculate the divergence and curl of the vector V = (- 4.9)(rz cos2(θ)) er + (- 6.8)(sin2(θ) + rz) eθ + ( 5.8)(rz + sin(θ)) ez at the point P ≡ ( 6.1, 0.4, - 4.3). (Round your answer to 2 decimal places.) Calculate the divergence and curl of the vector v = (- 4.9)(rz cos-(0)) e, +(-6.8) (sin (0) + rz) eg +(5.8) (rz + sin()) ez at the point P =( 6.1, 0.4. - 4.3). (Round your answer...