# Modification in Coulomb's Law and its implications

If the coulomb's law instead of following an inverse square relationship, follows an inverse cube relationship, How would it affect an isolated charged conducting sphere? How would it's field vary within the volume and how would the volumetric charge density be affected?
Please give in some valuable insights , would be helpful .

## Answers and Replies

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PeterDonis
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2019 Award
If the coulomb's law instead of following an inverse square relationship, follows an inverse cube relationship
It doesn't. Is there a particular reason why you are asking?

It doesn't. Is there a particular reason why you are asking?
It came up when I was attending my classes , that in some examination this concept was asked using a charged spherical conductor as mentioned above, the answer was told that it there will not be any electric field inside the bulk of the conductor which was quite intuitive, however the charge density was claimed to be non zero, which was quite counter intuitive as I believed charges would experience repulsion when present in the bulk, that's why I posted this to clear the doubt .

PeterDonis
Mentor
2019 Award
in some examination this concept was asked using a charged spherical conductor as mentioned above, the answer was told that it there will not be any electric field inside the bulk of the conductor which was quite intuitive, however the charge density was claimed to be non zero, which was quite counter intuitive as I believed charges would experience repulsion when present in the bulk
Can you post any math that was used? Normally here at PF we only discuss the actual theories of physics, not alternative theories; but I can see the point of an exam question like this if it is to show you why an inverse square law matches our actual experience where an inverse cube law would not. But the answer should be based on math, not intuition.

PeterDonis
Mentor
2019 Award
Moderator's note: moved to homework forum.