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Question
Gauss's law is true only if inverse square law for electric force between point charges is true . Think about this !
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Solution
- The key point is that Gauss' law works for forces that
emanate like lines of force out of the sources, whatever is their symmetry.
- To say that we have an inverse square force is to assume
each source is like a point in 3D space, so that its lines of force emanate in
all directions and the force acts like a surface density of those lines.
- We can make "Gaussian pillboxes" that conform to
whatever is the symmetry of our sources, so we don't always get an inverse
square force, but Feymann means we do if we regard each of our sources as a
point in 3D space, and then superimpose those points to get whatever is our
actual source symmetry.
- So if the force from a point source fell off like 1/r^3,
that could only act like the surface density of lines of force in 4 spatial
dimensions, so then Gauss' law would only work in 4 dimensions.
- The key point is that Gauss' law works for forces that emanate like lines of force out of the sources, whatever is their symmetry.
- To say that we have an inverse square force is to assume each source is like a point in 3D space, so that its lines of force emanate in all directions and the force acts like a surface density of those lines.
- We can make "Gaussian pillboxes" that conform to whatever is the symmetry of our sources, so we don't always get an inverse square force, but Feymann means we do if we regard each of our sources as a point in 3D space, and then superimpose those points to get whatever is our actual source symmetry.
- So if the force from a point source fell off like 1/r^3, that could only act like the surface density of lines of force in 4 spatial dimensions, so then Gauss' law would only work in 4 dimensions.
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