<0,0,w> L/2 A thin-walled hollow circular glass tube, open at both ends, has a radius R and a length L. The axis of the tube lies along the z-axis and the tube is centered on the origin. The outer sides are rubbed with wool and acquire a net negative charge -Q distributed uniformly over the surface of the tube. Use k for Coulomb's constant. To determine the electric field from the cylinder at location <0, 0, w> far from the tube, divide the tube into rings. An individual ring in the tube has thickness dz. A. How much charge dQ is on this ring? dQ Q.dz L B. Determine the relative position vector r for the given observation location and the center of a representative ring of charge located at <0, 0, z>. rx = 0 ry = 0 rz= W-Z C. Using your previous results, determine the infinitesimal electric field dỄ at the observation location for a single ring. Assume w >> L. dEx 0 dEy dEz = 0 Qk(w-z)dz L(R² + (w-z)²) D. Using the electric field you calculated above, determine the net electric field of the hollow tube at the observation location. This will require setting up and evaluating an integral. 0 Ex = Ey Ex = 0 = 20k RL -0.5 -0.5 4+ (L+2w) R² 4+ (L+2w)² R² ༡

<0,0,w> L/2 A thin-walled hollow circular glass tube, open at both ends, has a radius R and a length L. The axis of the tube lies along the z-axis and the tube is centered on the origin. The outer sides are rubbed with wool and acquire a net negative charge -Q distributed uniformly over the surface of the tube. Use k for Coulomb's constant. To determine the electric field from the cylinder at location <0, 0, w> far from the tube, divide the tube into rings. An individual ring in the tube has thickness dz. A. How much charge dQ is on this ring? dQ Q.dz L B. Determine the relative position vector r for the given observation location and the center of a representative ring of charge located at <0, 0, z>. rx = 0 ry = 0 rz= W-Z C. Using your previous results, determine the infinitesimal electric field dỄ at the observation location for a single ring. Assume w >> L. dEx 0 dEy dEz = 0 Qk(w-z)dz L(R² + (w-z)²) D. Using the electric field you calculated above, determine the net electric field of the hollow tube at the observation location. This will require setting up and evaluating an integral. 0 Ex = Ey Ex = 0 = 20k RL -0.5 -0.5 4+ (L+2w) R² 4+ (L+2w)² R² ༡

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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