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 tubelies along the x axis, with the left end at the origin. The outersides are 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 thetube into rings, of thickness dx. Consider arepresentative ring somewhere in the middle of the tube, with itscenter at . Draw a diagram illustrating this situation.
Step 2:
(a) How much charge dQ is on this ring? Write youranswer symbolically. (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 orsymbol stated 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.
