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- calculate the flux of the vector field through the given surface. ~F = z ~k through a square of side length 5 in the plane z = 2. The square is centered on the z-axis, has sides parallel to the axes, and is oriented in the positive z-direction.Compute the flux of the vector field F=2xi+2yj through the surface S, which is the part of the surface z=36−(x^2+y^2) above the disk of radius 6 centered at the origin, oriented upward. flux = _____Let f(x)= 4xex - sin(5x). Find the third derivative of this function. Note ex is denoted as e^x below. Select one: (12+4x^3)e^x + 125sin(5x) 12e^x + 125cos(5x) not in the list (12+4x)e^x + 125cos(5x) (8+4x)e^x + 25sin(5x)
- The figure here shows a Gaussian cube of face area Aimmersed in a uniform electric field that has the positivedirection of the z axis. In terms of E and A, what is the fluxthrough (a) the front face (which is in the xy plane), (b) therear face, (c) the top face, and (d) the whole cube?Find the shape of the free surface under constant ?? and ?? = −?.A large non-conducting slab of area A and thickness d has a charge density rho=Cx^4. The origin is through the center of the slab. That is to say, it bisects the slab into two equal volumes of d/2 thickness and with an area of A, with -d/2 to the left of x=0, and d/2 to the right of x=0. Express all answers in terms of C, x, and any known constants. Gaussian surface 1 (cylinder) is located such that its volume encompasses the charge contained within the slab. Apply Gauss's Law to cylinder 1 to determine the electric field to the left and to the right of the slab. Make sure you incude the domains over which the field is valid.
- Find the Miller Indices of a plane whose intercepts are (2,1,3).Reformulate Gauss’s law by choosing the unit normal of the Gaussian surface to be the one directed inward.Consider the field F(x,y,z)=2y j and the sphere centered at the origin of radius a. We can conclude that the flux of F through the sphere is:a. Twice the volume of the sphere b. sphere volume c. 5 times the volume of the sphered. 0