Field lines from a line of charge

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SUMMARY

The discussion centers on the application of Gauss's Law to determine the electric field around a cylindrical charge distribution. It is established that the electric field (E-field) radiates outward from the surface of an infinitely long cylinder, specifically in the radial direction (s-hat direction), with no longitudinal field lines along the z-axis. This phenomenon occurs because the electric fields produced by opposite points on the cylinder cancel each other out, leading to no net field along the cylinder's length. The neglect of the circular surface area in calculations is justified as there is no electric field passing through these circles, reinforcing the symmetry of the problem.

PREREQUISITES
  • Understanding of Gauss's Law in electrostatics
  • Familiarity with electric field concepts and vector fields
  • Knowledge of cylindrical symmetry in physics
  • Basic principles of electric field lines and their representation
NEXT STEPS
  • Study the derivation of Gauss's Law for different geometries, including spherical and planar symmetries
  • Explore the concept of electric field lines in finite charge distributions
  • Learn about the implications of symmetry in electrostatics and its applications
  • Investigate the behavior of electric fields in conductors and insulators
USEFUL FOR

Students of physics, educators teaching electrostatics, and professionals in electrical engineering seeking a deeper understanding of electric fields and Gauss's Law applications.

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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