Field lines from a line of charge

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Gauss' law indicates that the electric field from an infinitely long cylindrical charge distribution points radially outward, with no field lines along the cylinder's length. This occurs because electric fields from opposite sides of the cylinder cancel each other out, resulting in no net field along the z-axis. The surface area of the circular ends of the cylinder is neglected in calculations because there is no electric field passing through these areas. The symmetry of an infinitely long cylinder leads to the conclusion that the electric field is perpendicular to the circular cross-sections. Understanding these principles clarifies why field lines do not exist along the length of the cylinder.
vikasagartha
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I have a general gauss' law/electric field question.

In calculating the electric field of a cylindrical shape, gauss' law can be applied to find that the Electric field only points aways from the surface of the cylinder (aka, in the s-hat direction). But this means that there are no field lines directed along the cylinder...why isn't there a field line that points directly up or down along the z axis? For a finite cylinder, this would make sense to me. However, whenever you are calculating the E field via gauss' law, you neglect the surface area of the circles in the cylinder...can someone please clarify why this is? I have taken it for granted for a long time but never really understood...

Thanks in advance!
 
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vikasagartha said:
But this means that there are no field lines directed along the cylinder...
There are. But they get canceled out since two points on the conductor on either side of your point of consideration produce electric fields in opposite directions.
vikasagartha said:
..you neglect the surface area of the circles in the cylinder...can someone please clarify why this is?
Because there is no electric field passing through these circles. Reason same as above. Along the cylinder is nothing but perpendicular to these circles.
 
Gauss's law only helps if it is an infinitely long cylinder so that symmetry suggests there is no longitudinal E field.
 

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