Gauss's law and nonuniform electric field

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Homework Help Overview

The discussion revolves around applying Gauss's law to a nonuniform electric field represented by E=[-4i+(6+3y)j] N/C, with a Gaussian surface shaped as a cube of edge length 1.40 m. Participants are exploring the implications of treating part of the electric field as a constant vector and its effect on electric flux.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning why the constant vector component of the electric field does not contribute to the flux through the Gaussian surface. There is discussion about the nature of flux contributions from individual faces of the cube and the implications of integrating the normal component of the electric field.

Discussion Status

The conversation is ongoing, with participants seeking clarification on the treatment of the electric field components and their contributions to flux. Some guidance has been provided regarding the integration of the normal component and the behavior of the constant vector across opposite faces of the cube.

Contextual Notes

There is a focus on understanding the behavior of electric fields in relation to Gauss's law, particularly in the context of nonuniform fields and the assumptions made about constant vector contributions.

boredbluejay
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Homework Statement


A Gaussian surface is in the shape of a cube with edge length 1.40m. The electric field is E=[-4i+(6+3y)j]N/C.

I got an answer, but the solution manual stated that we treat the electric field as E=3yj+E0, where E0=-4i+6j, which does not contribute to the flux. Why is this? Please help!
 
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The flux of a constant vector is zero as the contribution from one side of the cube is positive and negative from the opposite side.

ehild
 
Ah, okay. I didn't know that. But when calculating the flux of individual faces, does the constant vector contribute?
 
You know how to get a flux of a vector field B(r) at an surface area A? you integrate the normal component of the vector B : Φ=∫BndA.
The normal component refers to the outward normal. Although there is nonzero flux from the constant vector on on side, there is the same with opposite sign on the opposite side.

ehild
 

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