Volume Charge Density in a long Cylinder

In summary, the conversation discusses a problem involving a long solid cylinder with a uniform charge distribution and a smaller cylindrical Gaussian surface inside the cylinder. The goal is to determine the enclosed charge in terms of the charge density, length, and radius of the Gaussian surface. The conversation also mentions confusion about the position of the Gaussian surface and using vectors to calculate the electric field. The conversation ends with a question about rearranging equations.
  • #1
MtHaleyGirl
6
0
I am never sure if I am on the right track when answering my homework problems. Anyway the problem involves a long solid cylinder of radius R and uniform charge distribution throughout its volume. We are supposed to choose a cylindrical gaussian surface of radius r and length L with r < R - so the gaussian surface is inside the cylinder. We are 1st supposed to determine q(enclosed) in terms of ρ (rho), L and r - and of course any other relevant constants. So first off - I am looking at the flux within the cylinder --- already I am nervous about this because I cannot think of how to imagine the flux within this cylinder... and then considering E ? So to further explain where I am at - since the cylinder is "very very long" I have capped off the gaussian cylinder inside the whole. 1st off - is q(enclosed) a ratio of the whole Q ? or is it constant within the cylinder (I don't think q = Q). I want to consider q/Q - where q = π(pi) r² L then Q = π R² L - then I want to take q/Q = (π(pi) r² L )/(π R² L ) - cancel the π(pi) and L to get q =(Qr²)/R² - then I wonder if I am getting anywhere = also does q = ρL - it shows in my book that q = λL (λ is linear charge density) and I don't know if it works for volume charge density too... :uhh: - feeling like a physics flunky...
 
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  • #3
Thanks, but I've been there - the gaussian surface is always shown outside the original cylinder, that is why I am confused... :confused:
 
  • #4
MtHaleyGirl said:
Thanks, but I've been there - the gaussian surface is always shown outside the original cylinder, that is why I am confused... :confused:

Recall that all you care about is the net charge INSIDE the Gaussian surface, so we can ignore anything outside the surface. To get the charge inside, just take the volume integral over the charge density.

-Dan
 
  • #6
No No No! :rofl: I've been to hyperphysics lots - the Gaussian surface is a cylinder within another cylinder. All of the examples I have seen the cylinder is used through a plane or around another cylinder. The Charged Cylinder is of radius R and the Gaussian surface is radius r r < R... Does that make sense? I'm no physics genius and when I am given a problem outside the regular examples I feel like my brain is being scrambled :yuck: - - - thanks though
 
  • #7
using vectors, i make the electric field E = -lamda/2pi(sqrt.[r^2-s^2])epsilon

r^2 = s^2 +(c-a)^2, (and b is c-a), therefore rearrange, (c-a)^2 is (r^2-s^2)

does this help?
 

What is volume charge density in a long cylinder?

Volume charge density in a long cylinder is the measure of electric charge per unit volume within the cylinder. It describes the distribution of electric charge within the cylinder and is typically denoted by the symbol ρ.

How is volume charge density calculated in a long cylinder?

Volume charge density in a long cylinder can be calculated by dividing the total charge within the cylinder by its volume. Mathematically, it can be expressed as ρ = Q/V, where Q is the total charge and V is the volume of the cylinder.

What factors affect the volume charge density in a long cylinder?

The volume charge density in a long cylinder is affected by the charge of the cylinder, the size and shape of the cylinder, and the material it is made of. It also depends on the presence of other charges or conductors in the vicinity of the cylinder.

How does volume charge density in a long cylinder relate to electric fields?

The volume charge density in a long cylinder is directly proportional to the electric field strength at any point inside the cylinder. This means that an increase in the volume charge density will result in a stronger electric field, while a decrease in the volume charge density will result in a weaker electric field.

What are the units of volume charge density in a long cylinder?

The units of volume charge density in a long cylinder are typically coulombs per meter cubed (C/m³) in SI units or coulombs per centimeter cubed (C/cm³) in CGS units. It can also be expressed in terms of other units such as ampere per meter squared (A/m²) or microcoulombs per milliliter (μC/mL).

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