iven the vector field A = x(^2)z i - 2y(^3)z^2 j + xy(^2)z k
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Given the vector field A = x(^2)z i - 2y(^3)z^2 j + xy(^2)z k . Solve for the div curl A
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- We 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 4.4.1bconsider the parallelepiped with sides: A=3i+2j+k، B=i+j+2k, c=i+3j+3k, then 1-Find the rolume of the paralldepiped 2-Find the area of the face determined by A and B. 3-Find the angle between the vactor C and the plane containing the face determined by A and BThe electric field in a region of space near the origin is given by E(z, y, :) – E, (*) yî+ xî a (a) Evaluate the curl Vx E(x, y, z) (b) Setting V(0, 0, 0) = 0, select a path from (0,0, 0) to (x, y, 0) and compute V (r, y,0). (c) Sketch the four distinct equipotential lines that pass through the four points (a, a), (-a, a), (-a, -a), and (a, -a). Label each line by the value of V.
- A long coaxial cable has a solid inner conductor with radius a and a hollow outer conductor with radius b. If the inner conductor has p = po/r, po conductor has-o, determine E for r > b. In(b-a) -(Po - σo)^ Eor -σ,b €o For (Poa ↑ σob) î const. and the outerCompute the flux of the vector field F = 2zk through S, the upper hemisphere of radius 5 centered at the origin, oriented outward. flux =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=