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. Determine the electric field at a location on the x axis, a distance w from the origin. Carry out all steps including checking your result. Explain each step. You may have to refer to a table of integrals. (Do this on paper. Your instructor may ask you to turn in this work.)

Explanation / Answer

surface area of cylinder=sc=2*pi*R(R+L)

chareg per unit area=Q/sc

area of ring=sr=pi*R2

chareg on ring=(Q/sc)*sr

distance of ring from observation=((w-x)2+R2)1/2

integral values are 0 to L

lower limit 0

upper limit L

part a)

if we consider the ring at mid point that is at (x,0)

then distance =d=w-x

part b)

vector from source(w,0) to obervation pt(0,R)

-()i^+Rj^

part c)

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