Can Volume and Linear Charge Densities Be Interchanged in Calculations?

[MtHaleyGirl]

OK, I may be out of my league here so feel free to let me know (in a nice way please) but conceptually & every other way I can come up with, I am trying to put together volume charge density, linear charge density and surface charge density ... for example in my text it says that in terms of a cylinder r(enclosed)=λh where λ is linear charge density and r is the radius of a cylinder - can I interchange ρ (for volume charge density) and λ such that r(enclosed) = ρh? - AND if I have a uniform charge distribution and I use a cylindrical gaussian surface enclosed in a larger cylinder (r for the gauss. cyl. < R -- the whole cylinder) does E(enclosed in the gauss. cyl.) = E as in the whole cylinder? Thats what Gauss's law is saying?? right?? and is q (enclosed) the same as Q(total)? ---- Thanks for any help - trying not to be a physics flunky ---- :shy:

 

[Astronuc]

See this discussion - http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elelin.html#c1

 

[kyle8921]

Hello! Don't worry, these concepts can be confusing at first but with some practice, you'll get the hang of it!

Volume charge density, linear charge density, and surface charge density are all different ways of describing the distribution of electric charge within a given space. Volume charge density (ρ) refers to the amount of electric charge per unit volume, linear charge density (λ) refers to the amount of electric charge per unit length, and surface charge density (σ) refers to the amount of electric charge per unit area.

In terms of a cylinder, we can use these different charge densities to describe the distribution of charge within the cylinder. For example, if we have a cylindrical object with a uniform charge distribution, we can use the linear charge density (λ) to describe the charge along the length of the cylinder. This is represented by the equation r(enclosed) = λh, where r is the radius of the cylinder and h is the height of the cylinder. This means that the amount of charge within the cylinder increases as we move further away from the center.

Now, to answer your question about interchanging ρ (volume charge density) and λ (linear charge density), the answer is no. These two quantities are not interchangeable because they represent different things. Volume charge density refers to the charge per unit volume, while linear charge density refers to the charge per unit length. So, in the equation r(enclosed) = ρh, ρ represents the amount of charge per unit volume, while in the equation r(enclosed) = λh, λ represents the amount of charge per unit length.

As for your question about Gauss's law, you are correct. Gauss's law states that the electric flux through a closed surface is equal to the total charge enclosed by that surface divided by the permittivity of free space. In your example, if you have a uniform charge distribution within a cylindrical Gaussian surface, the electric field (E) within the Gaussian surface will be the same as the electric field within the entire cylinder. This is because the electric field is dependent on the charge enclosed by the Gaussian surface, and in this case, the entire cylinder is enclosed by the Gaussian surface.

Finally, to answer your question about q (enclosed) and Q (total), they are not the same. q (enclosed) represents the charge enclosed by a specific surface, while Q (total) represents the total charge within the entire space.

I hope this helps clarify