IP Nas for the vector field (=.=) - deye where is the surface of region shown...
3) Consider the vector field F-ra where a is a constant vector and let V be the region in R3 bounded by the surfaces r y24,1, z0. Find the outward flux of F i1n across the closed surface S of V 3) Consider the vector field F-ra where a is a constant vector and let V be the region in R3 bounded by the surfaces r y24,1, z0. Find the outward flux of F i1n across the closed surface S...
Please only answer if you know how. Please show full workings. Regards (3) Consider the vector field Fa where a is a constant vector and let V be the region in R3 bounded by the surfaces2 +y2-4, 1,z-0. Find the outward flux of F onsider the vector ће across the closed surface S ofV. (3) Consider the vector field Fa where a is a constant vector and let V be the region in R3 bounded by the surfaces2 +y2-4, 1,z-0....
Problem 3: Surface integral. 1. Determine the surface integral of the vector field v = xł over S = {r ER3 | x2 + y2 + z2 = RP, and x > 0, z>0} by projecting the surface S onto the region A of the xy-plane (see lecture notes). Show that you obtain the correct result using spherical coordinates. What quantity did you actually calculate? 2. Calculate the flux of vector A through the surface S, where S = {x...
5. Surface integral of a vector field (10%) Consider the vector field F = fkır + ĉk2x. Evaluate the surface integral ſ F. ds over the surface of a closed cylinder about the z-axis specified by z = +3 and r = 2. (The cylinder has a height of 6 and a radius of 2.) The cylinder is illustrated below.
The plot of the vector field Fri+j is shown below. Is the vector field a conservative vector field? Yes, the vector field is conservative. O No, the vector field is not conservative.
Find the flux of the vector field F= {-y.x1) across the cylinder y=5x2, for 0 5x53.0 sz 1. Normal vectors point in the general direction of the positive y-axis Parametrize the surface using u=x and v=2. Set up the integral that gives the flux as a double integral over a region R in the ov-plane. JE-nas= |SO du v Type exact answers.) The fluxis (Simplify your answer)
13. (6 pts) FTLIs, Green's, and Divergence Theorems (a) Complete the table below. Theorem Need to check: FTLIs The vector field Il curve Il surface IS: Green's Theorem | The vector field II curve ll surface is: and: Divergence Theorem The vector field |l curve l surface is: (b) For each of the following, choose all correct answers from the list below that can be used to evaluate the given integral. List items may be used more than once. i....
upward 12) Avertical wire Carries current straight up in a region where the magnetic field Vector fonts toward the north. What is the direction of the magnetic free on this wone A.) downward Bij toward the northe C) toward the East Di) toward the west F.) toward the South
5. The electric field in a certain region of space is given by the vector field Vector E(Vector r)= Vector E(x,y,z)= (x-z)hatx+(z-y)haty V/m Find any two points P(x1,y1,z1) and Q(x2,y2,z2) such that the electric field at P is perpendicular to the electric field at Q. Evaluate the electric field at each of these two points. (Hint: Use the dot product.).
Ē There is an electric flux of 26.5 N·m²/C through the square region shown in the figure. Each side of the square has a length of 0.100 m, în is the unit vector normal to the plane of the surface, and the electric field is at an angle of 0 = 59.0° relative to the plane of the surface. A n Assuming that the field is uniform over the region shown, what is the magnitude E of the electric field?...