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f (electric flux) = EdA = Q/e, ?=-90.0µC/m
Solution says EA= ?l/e, E2prl=?l/e, E=?/2pre (next to laststep), E=2?/4pre (last step).
Please explain how got from next to last step to last step.Where do the 2 in the numerator and the 4 in the denominator comefrom.

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Elin Hessel
Elin HesselLv2
23 Nov 2019

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Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

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A uniform ladder is 13.0 m long and weighs 170 N. In Figure 12-76,the ladder leans against a vertical, frictionless wall at height h= 11.0 m above the ground. A horizontal force is applied to theladder at distance d = 2.6 m from its base (measured along theladder). If force magnitude F = 61 N, what are (a)x-,(b)y-components of the force of the ground on the ladder? If F =140 N, what are (c)x-, (d)y-components of the force of the groundon the ladder? (e) Suppose the coefficient of static frictionbetween the ladder and the ground is 0.48; for what minimum valueof the force magnitude F will the base of the ladder just barelystart to move toward the wall?

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.
Step 4:
Check the units, and the special case where w>>R.

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.

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