Gauss' law (1/r^3 instead of 1/r^2)

AI Thread Summary
If the electric field of a point charge were proportional to 1/(r^3), Gauss's law would not remain valid as it currently stands. The reasoning is based on the relationship between electric field strength and the surface area of a Gaussian surface. For a 1/(r^2) field, the flux through a spherical surface scales with the area, allowing for consistent application of Gauss's law. However, with a 1/(r^3) dependency, the flux would not scale appropriately with the surface area, leading to inconsistencies in the law's application. Thus, the fundamental principles underlying Gauss's law would be violated in this scenario.
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Homework Statement


If the electric field of a point charge were proportional to 1/(r^3) instead of 1/(r^2), would Gauss's law still be valid? Explain reasoning.


Homework Equations


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The Attempt at a Solution


Considered a spherical Gaussian surface centered on a single point charge.
 
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How would the flux through a sphere of radius one centered on the charge compare with the flux through a sphere of radius two?
 
What is true of the entire sphere is also true of any portion of its surface, I believe...
 
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