Solving Gaussian Problem: Cylindrical Shells w/ Radii R1 & R2

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In summary, the problem involves two cylindrical shells, one with a radius of 5.0 cm and a total charge of +4.2 µC, and the other with a radius of 9.0 cm and a total charge of -2.4 µC. The cylinders are 5.8 m long and the positive direction is away from the axis. The task is to find the electric field at three different radial distances from the central axis: 1.5 cm, 5.5 cm, and 11.5 cm. The equations used are E *Da = Qenclosed/Epsilon and point charge = 1/4pi epsilon * Q/r^2, and the answers are 0 N/C
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Katsmed23
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Homework Statement



A thin cylindrical shell of radius R1 = 5.0 cm is surrounded by a second cylindrical shell of radius R2 = 9.0 cm, as in the figure. Both cylinders are 5.8 m long and the inner one carries a total charge of Q1 = +4.2 µC and the outer one carries a total charge of Q2 = -2.4 µC. (Assume the positive direction is away from the axis.)

a) r = 1.5 cm
N/C

(b) r = 5.5 cm
N/C

(c) r = 11.5 cm
N/C


Homework Equations



E *Da = Qenclosed/Epsilon

point charge = 1/4pi epsilon * Q/r^2


The Attempt at a Solution



a) radius is smaller than the radius of the first shell, so it's EF = 0
b) I've tried using E = Q / 4pi *epsilon *r^2, but i keep getting the wrong answer = 12.4e6 N/C
c) I think I should add the charges together (-2.4 + 4.2 = 2uC) and use the above equation, but I am at a loss.

I keep trying to find the answers to these last 2, but can't seem to get it right.
 
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  • #2
do you need to find the E-field at the given r's, at the midplane of the cylinders?
 
  • #3
"For points far from the ends of the cylinders, determine the electric field at the following radial distances from the central axis."

yes sorry forgot to include that!
 

FAQ: Solving Gaussian Problem: Cylindrical Shells w/ Radii R1 & R2

What is the formula for calculating the volume of a cylindrical shell?

The formula for calculating the volume of a cylindrical shell is V = πh(R22 - R12), where h is the height of the shell and R1 and R2 are the inner and outer radii, respectively.

How do I determine the height of a cylindrical shell?

The height of a cylindrical shell is the difference between the outer and inner radii. In other words, h = R2 - R1.

Can I use this formula for any type of cylindrical shell?

Yes, as long as the shell has a circular cross-section and the radii are measured from the same center point, this formula can be used to calculate the volume.

How do I convert the units of the radii to match the units of the height?

To ensure that all units match, it is important to use the same unit of measurement for all values. For example, if the height is measured in meters, the radii should also be measured in meters.

Can this formula be used for partially-filled cylindrical shells?

Yes, this formula can be used for partially-filled cylindrical shells by simply adjusting the height (h) to represent the height of the filled portion. The radii (R1 and R2) should still be measured from the same center point.

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