Electric Flux depedent on position inside a surface, yes?

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Discussion Overview

The discussion revolves around the concept of electric flux, particularly in relation to a point charge placed inside a closed surface, such as a cubical Gaussian surface. Participants explore whether the position of the charge affects the electric flux through the surface and how the angle of the electric field with respect to the surface influences the flux calculation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions if the electric flux is dependent on the charge's position within the Gaussian surface, suggesting a lack of variable for position in the flux equation.
  • Another participant asserts that as long as the charge remains constant, the total electric flux does not depend on the charge's location or the surface's shape, provided it is closed.
  • A participant expresses skepticism about the logic of the assertion, noting that the flux equation does not include the angle of the electric field with respect to the surface.
  • It is pointed out that Gauss's law pertains to total flux and does not address flux through specific portions of the surface, implying that local flux may vary with charge movement.
  • Clarifications are made regarding the calculation of flux through small portions of the surface, emphasizing the role of the angle in the surface integral of the electric field.
  • Several participants refine their statements about the equations for total flux and local flux, indicating a progression in understanding the relationship between charge, electric field, and flux.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the implications of charge position on electric flux. While some maintain that total flux is invariant with charge location, others question the completeness of this view, particularly concerning local variations and the role of angle in flux calculations.

Contextual Notes

Participants acknowledge that the angle of the electric field relative to the surface is significant for local flux calculations, but this aspect is not included in the total flux equation. There are also indications of earlier misunderstandings regarding the equations used to describe electric flux.

Who May Find This Useful

This discussion may be of interest to students and professionals in physics, particularly those studying electromagnetism and Gauss's law, as well as individuals exploring the nuances of electric flux in relation to charge distribution and surface geometry.

rockyshephear
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Sample Problems to calculate Electric Flux

01. A point charge of 1.8mC is at the centre of a cubical Gaussain surface having each side 50cm. What is the net electric flux through the surface?

Suggested answer:
According to Gauss' theorem, flux = q / sigma sub0 or 1.8mC/8.854 x 10^-12

I would question if this is true no matter WHERE inside the cubical Gaussian surface the charge is. If it does matter, why is there no varible for the position inside a given surface?
 
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As long as the amount of charge inside the surface stays the same, the total electric flux through the surface does not depend on where the charge is located. It also doesn't depend on the size or shape of the surface, so long as the surface is closed.
 
Last edited:
I will take your word on that but it doesn't seem logical given the following.

Here's the equation for flux. Phi=q/sigma sub0

If this is true, flux has nothing at all to do with the radiating vectors' angle with respect to the surface they are passing through, since angle is not a part of the equation for flux.

So that sounds like these arrows can exit the surface at any angle as long as they pass through. As an analogy, a light blub in a glass sphere. The amount of light leaving the glass sphere is independent of the position of the bulb in the sphere.

So why is it stated that flux varies with how the surface faces the flow?

My question in a nutshell: Does flux vary wiith respect to the angle the field makes with the surface? If so, the why is the angle not included in the equation for flux?
Phi=q/sigma sub0
 
Note that Gauss's law only talks about the total flux; it makes no comment about the flux through any portion of the surface.

As you move the charge around within the surface, the field and thus the flux through some portion of the surface may certainly change, yet the total flux remains the same.
 
Oh, so the angle is only important with dA, flux thru a small portion of the overall surface.
So I can throw ANYTHING whatsoever in side the sphere and it's always zero?
 
Woops. I made a mistake. I mean whatever is inside the sphere is
Phi=q/epsilon sub0
but what is in a small portion is
Surface integral of vector E dot producted with vector dA
Is that better?
 
Another mistake. Rats.

I mean whatever is inside the sphere is
Phi=q/epsilon sub0
but what is in a small portion is
Surface E field times dA times cos theta =Vector E dot producted with dA
Is that better?
 
Yeah, that sounds right.
 
Or to be even more exact.

I mean whatever is inside the sphere is
Phi(total)=q/epsilon sub0
but what is in a small portion is
Phi(little chunk)=E field times dA times cos theta =Vector E dot producted with dA
Is that better?
 
  • #10
Sounds good.
 

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