How Is Electric Field Calculated for a Uniformly Charged Cylinder?

[i4nb63]

Homework Statement

Consider a long cylindrical charge distribution of radius R = 13 cm with a uniform charge density of ρ = 18 C/m3. Find the electric field at a distance r = 32 cm from the axis.

Homework Equations

ΦE = EA = qin/ε0

The Attempt at a Solution

My problem here is that I don't know how to solve it given uniform charge density. I can solve Gauss's law for a cylinder down to E = 2K(λ/r), but as I don't have a length, linear charge density doesn't help me much. So I'm stuck here, and any help would be great.

Thanks!
Ian

 

[Simon Bridge]

Apply Gauss' law: when you are a long way from the collection of charge, the field is the same as if all the charge were concentrated.

Do you know how to do it for a line of charge?

Q=ρV = ρAh
That help?

 

[i4nb63]

Φ = EA = Qin / ε

Qin = ρV = ρAh

EA = ρAh / ε

E = ρh / ε

Then I get stuck with h...

 

[Simon Bridge]

The electric field due to a short length dz of the cylinder will be the proportional amount of charge between z and z+dz and inversly proportional to the distance to the length. Use symmetry to cancel the z components and sum all the contributions along the entire cylinder.

You will have an example of an infinite line of charge someplace in your course notes.

Also see:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html