Electric field in all regions of infinite cylinder

[yayovio10]

Homework Statement

A uniform linear charge of λ is located along the z axis, and concentric circular cylinder of radius 2 [m] has a surface distribution charge of α . both distributions are infinite, the distribution of linear charge is contained in the interior of the circular cylinder as shown image.

λ = 3 * 10^-3 (C/M)
σ = 1.54pi * 10^-3 (C/M^2)

Determine E, in all regions

Homework Equations

The Attempt at a Solution

so i was wondering if these are the formulas that i have to use in order to solve this problem

 

[rude man]

You haven't identified a.

Is the red part a wire, a solid cylindrical dielectric section or a cylindrical shell section?

 

[yayovio10]

i think its a wire or a rod and "a" would be the radius of the cylinder, so my question would be since the problem gives you the surface charge of the cylinder

the total charge for r>a would be λL+ ρ*2∏*r*L ?

 

[rude man]

i think its a wire or a rod and "a" would be the radius of the cylinder, so my question would be since the problem gives you the surface charge of the cylinder

the total charge for r>a would be λL+ σ*2∏*r*L ?

No, the total charge (per length L) is not a function of r if r>a. Besides, you're supposed to find E(r).

I changed your "ρ" to a "σ".

 

[HalfLostAndSearching]

Yes, these are the formulas you would need to use to solve this problem. In order to determine the electric field in all regions of the infinite cylinder, you would need to use the formula for electric field due to a linear charge distribution, which is:

E = λ/2πεr

where λ is the linear charge density, ε is the permittivity of free space, and r is the distance from the linear charge.

For the surface distribution charge on the concentric circular cylinder, you would use the formula for electric field due to a surface charge distribution, which is:

E = σ/2ε

where σ is the surface charge density and ε is the permittivity of free space.

You would also need to take into account the fact that the linear charge is contained within the circular cylinder, so the distance from the linear charge would vary depending on the region you are considering.

Overall, to determine the electric field in all regions, you would need to use a combination of these formulas, taking into account the different distances and charge densities in each region.