<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 ŕ for the given observation location and the center of a representative ring of charge located at <0,0, z>. rx = ry = 0 Tz=0 C. Using your previous results, determine the infinitesimal electric field dỄ at the observation location for a single ring. Assume w >> L. dEx dEy dEz = 0 = 0 = 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. Ex = 0 Ey = 0 Ez =

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<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 ŕ for the given observation location and the center of a representative ring of charge located at <0,0, z>.
rx =
ry = 0
Tz=0
C. Using your previous results, determine the infinitesimal electric field dỄ at the observation location for a single ring. Assume w >> L.
dEx
dEy
dEz
= 0
= 0
=
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.
Ex = 0
Ey = 0
Ez
=
Transcribed Image Text:<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 ŕ for the given observation location and the center of a representative ring of charge located at <0,0, z>. rx = ry = 0 Tz=0 C. Using your previous results, determine the infinitesimal electric field dỄ at the observation location for a single ring. Assume w >> L. dEx dEy dEz = 0 = 0 = 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. Ex = 0 Ey = 0 Ez =
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