# Electric field everywhere for a hollow cylindrical conductor?

1. Dec 2, 2016

### Vitani11

1. The problem statement, all variables and given/known data
An infinitely long, hollow, conducting cylinder has a inner radius a and outer radius b and carries a linear charge density λ along its length. What is the electric field everywhere?

2. Relevant equations
∫E⋅dA = Qenc/∈

Variables
∈ = permittivity constant
λ = linear charge density
E = electric field
r = distance to point of E field
Qenc = enclosed charge

3. The attempt at a solution
For inside (r∠a) and in the shell (a∠r∠b) the electric field is zero. I don't know what to do for outside the shell. I think the charge is concentrated on the outer shell just as for a spherical conductor, is this true? Here is my attempt for outside.

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2. Dec 2, 2016

### Dilemma

Use Gauss's law:
∫E⋅dA = Q / ∈

E ⋅ (2πrL) = λ * L / ∈ where L denotes the imaginary Gaussian surface's length.

Therefore,

E = λ / (2π∈r)