Is My Integral Setup Correct for the Electric Field of a Square Sheet?

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SUMMARY

The integral setup for calculating the electric field of a square sheet is confirmed to be correct. The equation used is \(\vec{E} = \sigma z \int_{-a/2}^{a/2} \int_{-a/2}^{a/2} \frac{dx' \, dy'}{(x'^2 + y'^2 + z)^{3/2}} \hat{z}\). It is noted that in the SI system, an overall factor of \(k = \frac{1}{4\pi\epsilon_0}\) should be included. This confirms the proper formulation for deriving the electric field from a uniformly charged square sheet.

PREREQUISITES
  • Understanding of electric fields and charge distributions
  • Familiarity with double integrals in calculus
  • Knowledge of the SI unit system and constants like \(\epsilon_0\)
  • Basic principles of electrostatics
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  • Study the derivation of electric fields from different charge distributions
  • Learn about the application of the Coulomb's law in electrostatics
  • Explore the concept of potential energy in electric fields
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Students studying electromagnetism, physics educators, and anyone involved in electrostatics or electric field calculations.

Shinobii
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Homework Statement


Field the electric field of a square sheet. I understand this is a simple problem, I just want to confirm I have the integral set up correctly.


Homework Equations


[tex]\vec{E} = \sigma z \int_{-a/2}^{a/2} \int_{-a/2}^{a/2} \frac{dx' \, dy'}{(x'^2 + y'^2 + z)^{3/2}} \hat{z}.[/tex]

I just want to double check if I have set up the integral correctly.
 
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Looks good to me! [EDIT: In SI system there would be an overall factor of ##k = \frac{1}{4\pi\epsilon_0}##]
 
Last edited:

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