Electrical flux passing through the cube

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SUMMARY

The discussion focuses on calculating the electric flux through a cube using Gauss's Law, specifically addressing the challenge of avoiding cylindrical symmetry. Participants emphasize that the relevant equation for this scenario is the electric flux equation, which states that the flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space (Φ = q / ε0). The conversation highlights the importance of symmetry in simplifying the integration of the electric field across the cube's surfaces.

PREREQUISITES
  • Understanding of Gauss's Law in electromagnetism
  • Familiarity with electric flux concepts
  • Basic knowledge of electric fields and charge distributions
  • Ability to perform surface integrals in vector calculus
NEXT STEPS
  • Study the application of Gauss's Law in various geometries, focusing on cubes
  • Learn about electric field calculations for different charge distributions
  • Explore symmetry in electric fields and its implications for flux calculations
  • Review vector calculus techniques for surface integrals
USEFUL FOR

Students and professionals in physics, particularly those studying electromagnetism, as well as educators seeking to enhance their understanding of electric flux and Gauss's Law applications.

MatinSAR
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Homework Statement
Consider a rod with an electric charge density λ that passes through the center of the cube. Prove that the electric flux passing through this cube is equal to = q / ε0
Relevant Equations
Gauss's law
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Picture for better understanding.
My answer :
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I want to know how to solve this problem without using cylindrical. I mean how can we solve this using cube and its sides.
Thanks.
 
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MatinSAR said:
Relevant Equations:: Gauss's law

I want to know how to solve this problem without using cylindrical. I mean how can we solve this using cube and its sides.

What about your relevant equation ?

##\ ##
 
BvU said:
What about your relevant equation ?

##\ ##
Thank you ... but what do you mean by relevant equation?
 
Does your relevant equation worry about the shape of the surface ?

[edit]On the other hand,
Prove that the electric flux passing through this cube is equal to = q / ε0
could be interpreted as an invitation to show that for this case the gauss identity holds. In that case you could actually integrate the flux: you know the electric field (right?) and can benefit from symmetry.

##\ ##
 
Last edited:
BvU said:
Does your relevant equation worry about the shape of the surface ?
I guess no it doesn't ... Thank you for your help ...
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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