2) A thin cylindrical shell of radius R and height h is placed in the xy plane with its base at the origin. The cylinder has a uniform o charge density, find the electric field at point P on its z axis (Use E = k). Z P
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- 1. The electric field in a region of space near the origin is given by () E(x, y, z) = Eo a (a) Evaluate the curl V x 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 (x, y, 0).2. Find the electric field at a distance z above the center of a ring of radius a that has a uniform linear charge density A. Compute (only) the Er and Ez components of a cylindrical coordinate system.b) A uniformly charged rod has length L and charge Q as shown below. P a L (i) Find the electric field vector at point P above center of rod. The distance from center of rod to point P is a. (ii) Using the results from part (i) above, show that for an infinite rod (L → ∞) the electric field at point P is given by E = 2te,a where 1 = Q/L is the linear charge density.
- Problem 3 Consider a ring and a disk parallel to each other with their central axes along a common line. The disk, located at the origin (point O), has a uniform charge density σ =-5 nC/m² and radius Rdisk 11 m. The ring, located at x=d, has a uniform charge Gring -1 nc and radius Ring -9 m. The magnitude of the total electric field at the center of the ring (point A) is E-157 N/C Disk Ring d Ө Find the charge of the disk disk B Find the linear charge density of the ring Aring" Find the distance between the ring and the disk d= The total electric field vector Etat at x = d is in the direction. The total electric field vector Etotal at x=d+2 is in the direction. Find the electric field magnitude at point B located 9 m from point A, due to the ring only Ering 7. Find the electric field magnitude at x = 15 m from the origin, due to the disk only EdiskO Macmillan Learning A sphere of radius R = 0.290 m and uniform charge density -151 nC/m³ lies at the center of a spherical, conducting shell of inner and outer radii 3.50R and 4.00R, respectively. The conducting shell carries a total charge of Q = 14.3 nC, Determine the magnitude E(r) of the electric field at the given radial distances r from the center of the charge distribution. E (0.260R) = E (3.90R) = = E (1.85 R) = N/C N/C N/C R 3.50R 4.00RGiven a non-uniform SURFACE charge density o= ko r z cos q, ko constant, r, o,z are cylindrical coordinate variables 12. Find the total "Q" placed on a closed cylinder of radius "R" and length "L" centered on the origin with one base in the x-y plane, along the positive z-axis.