A hollow glass tube A thin-walled hollow circular glass tube, open at both ends,

Question

A hollow glass tube A thin-walled hollow circular glass tube, open at both ends, has a radius R and length L (see the figure). The axis of the tube lies along the x axis, with the left end at the origin. The outer sides are rubbed with silk and acquire a net positive charge Q distributed uniformly. Since we know the electric field of a charged ring, divide the tube into rings, of thickness dx. Consider a representative ring somewhere in the middle of the tube, with its center at (x,0,0).

What is the vector from source to observation location?

Comment:

I'm not sure how to define the source as a vector.

My first guess was the source is <0,rsin0,-rcos0> because of the book example-wronge! :(I think I'm on my last try, please help!

Explanation / Answer

surface charge density=s=(Q/2piRL), from symmetry E points along x-axis, E=(1/4pik)?(from x=0 to L) (1/((R/2)^2 +(w-x)^2))*((w-x)/v(R/2)^2 +(w-x)^2)(Q/2piRL)(2piR) dx =(1/4pik)?(from x=0 to L) ((w-x)/((w-x)^2 +(R/2)^2)(3/2))*(Q/L) dx =(Q/4pikL)?(from x=0 to L) -(s/(v(s^2 +(R/2)^2)(3/2)) ds, s=w-x

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