Solving an Electric Field Due to an Infinite Cylinder

[TrolliOlli]

Homework Statement

An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density
ρ = 200 nC/m^3 What is the electric field at r = 8.0 cm

Homework Equations

I'm confused as to how to do this problem, I've tried converting from volume charge density to simply charge density λ and then solving with the equation for the E field due to an infiinite line charge, but this doesn't give me the right answer.

The Attempt at a Solution

(200 x10 ^-9)((4/3)(pi)(.04^3)) = Q

λ = Q / L so λ = Q (as we're taking L to be 1 meter in the above equation)

Efield due to infinite line charge= 2kλ/(.08)

the correct answer is supposed to be .23kN/c

 

[SammyS]

It looks like there is enough symmetry to use Gauss's Law.

 

[TrolliOlli]

It looks like there is enough symmetry to use Gauss's Law.

I know but I tried finding Q as I showed above, by taking ρ = 200nC/m^3 and multiplying it by the volume (4/3 pi (.04)^3) to get Q = 5.36E-11

I then use Gauss's law: E(4pi(.08)^2) = 5.36E-11/ε₀

this however gives me E = 75.306

What am I doing wrong?

 

[SammyS]

(4/3)πR³ is the volume of a sphere of radius, R.

You should be working with a cylinder.

 

[TrolliOlli]

Edit: never mind I found the answer, Thanks again for the help.

 

[SammyS]

A cylinder of height 1 m is OK. A radius of 4 cm will give you the charge enclosed by a cylinder of height 1 m and radius of 8 cm, which is your Gaussian surface.