Electric field on a point around a finite wire

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SUMMARY

The discussion focuses on calculating the electric field around a finite linear wire with a uniform charge density (λ) located along the Z-axis, specifically between points z1 = a and z2 = b. Participants suggest using Gauss's Law, represented by the equation ##\oint_S {E dA = \frac{1}{{\varepsilon _0 }}} Q##, to derive the electric field vector ##\vec{E}(\vec{r})## at point P and to determine the angle between ##\vec{E}(\vec{r})## and the polar versor ##\hat{r}(\varphi)##. A Hyperphysics resource is recommended for further understanding of electric fields related to linear charge distributions.

PREREQUISITES
  • Understanding of Gauss's Law and its application in electrostatics
  • Familiarity with electric field concepts and vector notation
  • Knowledge of cylindrical coordinates and their use in physics
  • Basic principles of charge density and its implications on electric fields
NEXT STEPS
  • Study the application of Gauss's Law in different geometries, particularly linear charge distributions
  • Explore the derivation of electric fields from continuous charge distributions
  • Learn about the relationship between electric fields and potential energy in electrostatics
  • Investigate the use of Hyperphysics and similar resources for solving electrostatics problems
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone seeking to understand electric fields generated by linear charge distributions.

flivon
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Homework Statement


In the figure below, there is a linear rectilinear uniform wire with charge density of ## \lambda ##. It its located at the Z axis, where z1 = a and z2 = b, (b> a)
The point O is the origin of the coordinates. "R" is the cylindrical polar radial coordinate.

a) Find the ##\vec{E}(\vec{r})## in the point P
b) Determine the angulus between ## \vec{E}(\vec{r})## and the polar versor ## \hat{r}(\varphi )##
71z91KN.png

Homework Equations


Gauss Law maybe?
##\oint_S {E dA = \frac{1}{{\varepsilon _0 }}} Q##

The Attempt at a Solution


I honestly don't have any ideia on how to solve this. Do you guys know some material where I can find something similar?
 
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