Calculate the flux of the vector field F(x, y, z) = 5i + 5j + zk through the closed circular cylinder of radius 4 centered about the z-axis for -6 ≤ z ≤ 6, oriented away from the z-axis. Note: a closed cylinder has a top and a bottom. Flux = SS F.dĀ=
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- A charge q1 of 38 µC is placed at the origin of the xy-coordinate system and a charge q2 of -62 µC is placed on the positive x-axis at x = 29 m. Calculate the flux passing the rectangle of dimensions 5 cm by 19 cm normal to the electric field at at point (29 m, 29 m) in N • m2/C. Please answer.What is the net outward flux of the radial field F = ⟨x, y, z⟩across the sphere of radius 2 centered at the origin?Six negative charges and two positive charges, all of equal magnitude Q, are arranged as shown in the Fig. A. The radius of the circle is r. The magnitude of the electric field generated by a single charge Qis, E = 150 N/C at the origin. (a) What is the magnitude of the net electric field at the origin O. (b) What is the direction of the net electric field? Choose from the arrows shown in Fig. B. -Q D* 0 Fig. B -Q' Fig. A Your Answer: (a) Magnitude: (b) Direction: (Choose from the arrow).
- Question 1 Four stationary electric charges produce an electric field in space. The electric field depends on the magnitude of the test charge used to trace the field O has different magnitudes but same direction everywhere in space is constant everywhere in space has different magnitude and different directions everywhere in space CANADA uniform electric field measured over a square surface with side length d = 15.5 cm makes an angle θ = 67.0° with a line normal to that surface, as shown in the figure below. There is a square horizontal surface with length and width d. The surface has a normal vertical axis at the center with a vector labeled vector E traveling from the center of the plane up and to the right. Vector E and the normal vertical axis form an angle labeled θ. If the net flux through the square is 5.40 N · m2/C, what is the magnitude Eof the electric field (in N/C)? N/CConsider a triangle in the presence of a uniform electric field given by 5.6 i N/C. The endpoints of the triangle are: (0 m, 0 m, O m), (7 m, O m, 4 m), and (2 m, 3 m, O m). Determine the absolute value of the electric flux through the triangle. Give your answer in units of N-m?
- Consider the vector field ʊ(r) = (x² + y²)êx + (x² + y²)êy + z²êz. Decompose the vector field (r) into the sum of two other vector fields, a (r) and 5(r), such that a(r) has no divergence (it is solenoidal) and 5 (r) has no curl (it is irrotational). The answer is not unique. This is the Helmholtz decomposition.In free space, let D = 8xyz4ax + 4x2z4ay + 16x2yz3 az pC/m2.Find the total electric flux passing through the rectangularsurface z = 2, 0 < x < 2, 1 < y < 3, in the az direction. Find Eat P(2, −1, 3).Calculate the flux of the vector field F(x, y, z) = (5x + 8)i through a disk of radius 7 centered at the origin in the yz-plane, oriented in the negative x- direction.
- = Let er be the unit radial vector field. Compute the outward flux of the vector field F er/r² through the ellipsoid 4x² + 6y² + 9z² = 36. [Hint: Because F is not defined at zero, you cannot use the divergence theorem on the bounded region inside of S. ]Consider a solid uniformly charged dielectric sphere where the charge density is give as ρ. The sphere has a radius R. Say that a hollow of charge has been created within the spherethat is offset from the center of the large sphere such that the small hollow has its center on the x axis where x = R/2. Using a standard frame where the large frame has its center at the origin, find the Electric field vector at the following points. a.The origin b.Anywhere inside the hollow (challenging) c.x = 0, y = R d.x = -R, y =0We have calculated the electric field due to a uniformly charged disk of radius R, along its axis. Note that the final result does not contain the integration variable r: R. Q/A 2€0 Edisk (x² +R*)* Edisk perpendicular to the center of the disk Uniform Q over area A (A=RR²) Show that at a perpendicular distance R from the center of a uniformly negatively charged disk of CA and is directed toward the disk: Q/A radius R, the electric field is 0.3- 2€0 4.4.1b