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.A circular ring of radius a and uniform charge density a is bent along diameter to make to halves perpendicular to each other electric field at the centre of bent ring is 2KN (a) 2KA (b) 2/2KN (C) 4/2KA (p) a. a Another noint charge
- 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.2R The center of the charged eircle of radius R = 30cm in the x-z plane is coincident with the origin of the coordinate system in the figure. The total charge Qon the circle is not uniform, but is distributed according to the relation A=v50 Where 0 is the angle between the radius R of the cirele and the +x-axisin radian. Find the magnitude of the Electric field due to these charges in they-axis direction only, at the point P at a distance of 2R. k, 9x 10 () and n 3 () b» - C) ) () () () 10 10 a) 10 1013 105 ) e 75 ini nören(b) It was measured that the electric field at point P with magnitude 450 N/C just outside the outer surface of a hollow spherical conductor. The direction of the electric field is directed outward. The hollow spherical conductor has an inner radius of 15 cm and outer radius of 30 cm. After that, another particle with unknown charge Q is put at the center of the sphere, the electric field at point P is still directed outward but the magnitude of the electric field decreased down to 180 N/C. i. Calculate the net charge enclosed by the outer surface before particle Q was introduced ii. Calculate charge Q After charge Q was introduced, iii. Determine the charge on the inner surface of the conductor iv. Determine the charge on the outer surface of the conductor
- 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 4.00Rc) A cube of side 50cm and it placed in a uniform electric field E = 4ĵ +2k . Find out [2] CO3 electric flux for all faces of the cube. [ You must draw the cube with axes]
- Given 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.6) The hollow R radius cylindrical tube is infinitely long along the z-axis. The positive charges are evenly distributed over the surface of the tube, and the surface charge density σ. Find electric fields in both regions accordingly. A) r<R for D=0; r>R for D=arσR/r B) None. C) r<R for D=0; r>R for D=arσR/((\pi\)r) D) r<R for D=0; r>R for D=arπσR/r E) r<R for D=0; r>R for D=0 this is an electromagnetic wave lesson question.Figure shows a point charge Q=2 nC placed at origin and a very long line carrying free charge with charge density, p, of +0.5 nC/m placed normal to the xy-plane at coordinate x = - surrounding is free space, state Gauss's Law and use it to determine the electric field at point P (0, 0.03, 0). All distances are in meters. -0.04 m. Assuming that the Q = +2 nC Line Charge