A thin-walled hollow circular glass tube, open at both ends, has aradius R and length L (see the figure). The axis of the tube liesalong the x axis, with the left end at the origin. The outer sidesare rubbed with silk and acquire a net positive charge Qdistributed uniformly. Determine the electric field at a locationon the x axis, a distance w from the origin. Carry out all stepsincluding checking your result. Explain each step. You may have torefer to a table of integrals.
Step 1: Since we know the electric field of a charged ring, divide the tubeinto rings, of thickness dx. Consider a representative ringsomewhere in the middle of the tube, with its center at . Draw adiagram illustrating this situation.
Step 2: (a) How much charge dQ is on this ring? Write your answersymbolically. (Use any variable or symbol stated above asnecessary.)
dQ = ________
(b) What is the distance from this ring to the observationlocation?
d = ________
(c) What is the vector from the source to observationlocation?
r = ________ (this answer is a vector)
(d) What is the integration variable? (Use any variable or symbolstated above as necessary.)
answer = ________
(e) What is the lower integration limit? (Use any variable orsymbol stated above as necessary.)
answer = ________
(f) What is the upper integration limit? (Use any variable orsymbol stated above as necessary.)
answer = ________
Step 3: Evaluate the integral, using the tool of your choice.
Step 4: Check the units, and the special case where w>>R.
