Is the Electric Field Zero Inside an Infinitely Long Cylinder?

[kasse]

[SOLVED] Electric field around cylinder

Homework Statement

An infinitely long cylinder with r = 4.0 cm has a uniform charge density of 200 nC/m^3. What is the electric field 3.9 cm away from the axis?

The Attempt at a Solution

The first thing I thought is that the field has got to be 0 since all the charge will be on the surface of the cylinder. But maybe this applies only to spheres?

Anyway, I calculated the charge per meter: 1.01 nC/m. Then I used Gauss law:

Q/l = e₀E*2*pi*r, which yields

E = (Q/l)/(2*pi*r) = 0.47 kN/C

Is this correct?

 

[alphysicist]

Hi kasse,

About the charges being on the surface: If this was a conductor (so that the charges could move) then the charges would be on the surface. However, here the charges are uniformly spread throughout the cylinder and cannot move.

When you draw your Gaussian surface at 3.9 cm from the axis, you have to take into account that some of the charges are outside the Gaussian surface and some are inside; only those charges that are enclosed in the Gaussian surface will appear in Gauss's law.

 

[kasse]

Well explained. Thanks!