Electric field everywhere for a hollow cylindrical conductor?

  • Thread starter Vitani11
  • Start date
  • #1
275
3

Homework Statement


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?

Homework Equations


∫E⋅dA = Qenc/∈

Variables
∈ = permittivity constant
a = inner radius
b = outer radius
λ = linear charge density
E = electric field
r = distance to point of E field
Qenc = enclosed charge

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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Answers and Replies

  • #2
15
1
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)

I hope this was helpful.
 
  • #3
275
3
That is exactly what I did in the picture. Great - thank you!
 

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