Question

A positively charged disk of radius R-0.0276 m and total charge 53.8 HC lies in the xz plane, centered on the y axis (see figure below). Also centered on the y axis is a charged ring with the same radius as the disk and a total charge of -35.1 HC. The ring is a distance d-0.0050 m above the disk. Determine the electric field at the point P on the y axis, where P is y 0.0100 m above the origin. (Express your answer in vector form.) N/C

Answer 1

Electric field on axis of a charged disk E_disk = 2 pi k sigma(1 - x/(x^2 + R^2)^1/2) sigma = Q/pi R^2 = charge density here E_disk = 2 pi k Q_disk/pi R^2 [1 - y/(y^2 + R^2)^1/2] electric field on axis of a charged ring E_ring = k x Q_ring/(x^2 + R^2)^3/2 where x = distance between eq here = k(x - d) Q_ring/((y - d)^2 + R^2)^3/2 E_ring = 2 k Q_disk/R^2 [1 - X/(y^2 + R^2)^1/2] + k(x - d) Q_ring/((y - d)^2 + k^2)^3/2 = 2 times 9 times 10^9 times 53.8 times 10^-6/(0.0276)^2 (1 - 0.0100/squareroot (0.01)^2 + (0.0276)^2] + 9 times 10^9 times (0.01 - 0.005) times 53.8 times 10^-6/((0.01 - 0.005)^2 + (9 times 10^9)^2)^3/2 (12712.66 times 10^3 times 0.66) + (2.42 times 10^3) E_ring = 8.39 times 10^6 N/C