Is Left Side of Gauss' Law equation not the total electric flux?

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SUMMARY

The discussion centers on the application of Gauss' Law to determine the charge enclosed by a cubical box with a total electric flux of 4700 Nm²/C. The misunderstanding arises from the interpretation of the left side of Gauss' Law, which represents the total electric flux, not the charge itself. The correct approach is to use the equation Q_enclosed = total electric flux * ε₀, where ε₀ is the permittivity of free space, a constant value. The size of the box is irrelevant for this calculation.

PREREQUISITES
  • Understanding of Gauss' Law and its mathematical formulation
  • Familiarity with electric flux and its units (Nm²/C)
  • Knowledge of the permittivity of free space (ε₀)
  • Basic principles of electrostatics
NEXT STEPS
  • Calculate the charge enclosed using Q_enclosed = total electric flux * ε₀
  • Explore the implications of different shapes in Gauss' Law applications
  • Study the concept of electric field vectors and their integration over surfaces
  • Review examples of electric flux calculations in various geometries
USEFUL FOR

Students of physics, particularly those studying electromagnetism, educators teaching Gauss' Law, and anyone seeking to clarify concepts related to electric flux and charge calculations.

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Homework Statement



The total electric flux from a cubical box 40.0 cm on a side is 4700 Nm^2/C. What charge is enclosed by the box?

Homework Equations



Gauss Law: surface integral of E-field-vector * dA-vector = Q_enclosed/epsilon naught

The Attempt at a Solution



The reason I am making this post is that I was under the impression that the left side of Gauss' Law is the total (or net) electric flux over the surface of the shape. Why am I even being given the sides of the box? 4700 Nm^2/C, being the total electric flux, is the left side of the equation in Gauss' Law!

Why is my answer of [4700 * epsilon naught] incorrect?

Thanks.
 
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DocZaius said:

Homework Statement



The total electric flux from a cubical box 40.0 cm on a side is 4700 Nm^2/C. What charge is enclosed by the box?

Homework Equations



Gauss Law: surface integral of E-field-vector * dA-vector = Q_enclosed/epsilon naught

The Attempt at a Solution



The reason I am making this post is that I was under the impression that the left side of Gauss' Law is the total (or net) electric flux over the surface of the shape. Why am I even being given the sides of the box? 4700 Nm^2/C, being the total electric flux, is the left side of the equation in Gauss' Law!

Why is my answer of [4700 * epsilon naught] incorrect?

Thanks.
That answer is right, but remember that ε0 is a number. You should be able to give your answer in Coulombs.

Also, you are right in saying you don't need the size of the box.
 

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