Deriving V-E Relation for Uniformly Charged Rod at Radial Distance r > a"

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SUMMARY

The discussion focuses on deriving the relationship between electric potential (V) and electric field (E) for a uniformly charged rod at a radial distance (r) greater than its radius (a). Participants emphasize the application of Gauss' Law to determine the electric field (E) and the relationship E = -dV/dr to find the potential (V). The fundamental equation \(\vec E = -\nabla \Phi\) is highlighted as essential for understanding the derivation process. The conclusion is that both concepts are interconnected through calculus and electrostatic principles.

PREREQUISITES
  • Understanding of Gauss' Law in electrostatics
  • Familiarity with electric potential and electric field concepts
  • Basic calculus, particularly differentiation
  • Knowledge of vector calculus, specifically gradient operations
NEXT STEPS
  • Study the application of Gauss' Law for cylindrical symmetry
  • Learn about the relationship between electric field and potential in electrostatics
  • Explore vector calculus, focusing on gradient and divergence
  • Investigate examples of electric fields generated by charged objects
USEFUL FOR

Students of physics, electrical engineers, and anyone interested in electrostatics and field theory will benefit from this discussion.

SpatialVacancy
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Could someone help me out on this problem?

Derive a relation between the potential [itex]V[/itex] and the magnitude of the Field [itex]E[/itex] at a radial distance [itex]r[/itex] from the axis
of a very long uniformly charged rod of radius [itex]a[/itex] ([itex]r > a[/itex]).
 
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I'm not following that properly. At first I would have thought you use Gauss' Law for electrostatics to work out the E field at a point r from the rod and then use E = -dV/dr, but that doesn't seem right :/.
 
I'm not sure what you mean by "derive a relation between..." since [itex]\vec E = -\nabla \Phi[/itex] is fundamental.
 

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