Electric Field within Cylinder

In summary, the problem involves finding the electric field at two different positions, one inside and one outside a long cylinder with a uniform fixed charge density. The electric field can be calculated using Gauss's Law, which states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space. For the first position, the electric field is found to be -800 N/C, while for the second position it is 770 N/C. However, the calculation for the second position seems to be incorrect and further guidance is needed.
  • #1
hoarhaykoobas
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0
Electric Field within Cylinder - Gauss's Law

Hi, I am new to this forum. I am dying over this problem. Any help would be greatly appreciated.

1. A long cylinder has a uniform fixed charge density [tex]\rho=-8.3\times 10^{ - 7} C/m^3[/tex]. The region outside the cylinder carries no charge. The radius of the cylinder is 0.024m.
(a) What is the electric field at a position inside the cylinder marked "x" which is 0.017m away from the center line of the cylinder? A: -800 N/C
(b) What is the electric field at a position outside the cylinder marked "y", which is 0.035m away from the center line of the cylinder? A: 770 N/C


2. Gauss's Law: [tex]\phi= \frac{\sigma A}{\epsilon_{0}}[/tex]
3. The closest I got to the answer to part (a) is as follows:[tex] \\ Q=\rho\times A\times d=-5.11\times 10^{-11}[/tex][tex] E=K_{e}\frac{Q}{r^2}=-797.55 N/C[/tex]
Part (b) i just can't seem to apply the same method, which i believe is pretty flawed to begin with.
*My textbook doesn't cover this too deeply and my professor gave this to us as a supplemental problem.

After getting nowhere with the electric flux equations and it's diff forms for part (b), I found this page, which seemed to be exactly what I was looking for but i keep getting the wrong answer: http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/elecyl.html" [Broken]
 

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  • #2
Gauss's Law is the correct way to do this problem. Can you show your work? I can't find you mistakes if I can't see your work.
 
  • #3
I updated my question. I'm sorry about that. I hope it's easy to see what I'm doing wrong. I've included a jpeg of the problem. Thanks so much
 

1. What is the formula for calculating the electric field within a cylinder?

The formula for calculating the electric field within a cylinder is E = λ/2πεr, where λ is the linear charge density, ε is the permittivity of the material, and r is the distance from the center of the cylinder.

2. How does the electric field within a cylinder vary with distance from the center?

The electric field within a cylinder varies inversely with the distance from the center. This means that as the distance increases, the electric field decreases.

3. Is the electric field within a cylinder affected by the material it is made of?

Yes, the electric field within a cylinder is affected by the material it is made of. This is because the permittivity of the material affects the strength of the electric field.

4. Can the electric field within a cylinder be negative?

Yes, the electric field within a cylinder can be negative. This can occur if the linear charge density and the distance from the center are such that the formula for the electric field results in a negative value.

5. What is the direction of the electric field within a cylinder?

The direction of the electric field within a cylinder is radial, meaning it points directly away from or towards the center of the cylinder depending on the charge distribution. If the charge is evenly distributed, the electric field will be pointing in the same direction at all points on the cylinder's surface.

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