Inverse-Square Law: Isotropic vs Anisotropic Radiation

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The discussion centers on the inverse-square law of electromagnetic radiation, specifically addressing why the law is expressed as 1/(r^2) rather than P/(4π(r^2)). Participants clarify that the 4π factor can be integrated into the constants used in the inverse-square law, affirming that radiation propagates isotropically in all directions. Additionally, there is a proposal to utilize natural Planck Units that normalize 4πG and a charge unit that normalizes ε₀, enhancing the understanding of these constants in physics.

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If the intensity of electromagnetic radiation (I) is equal to the power emitted (P) divided by the area of the sphere (4pi(r^2)) that it radiates, why is the inverse-square law 1/(r^2) instead of P/(4pi(r^2))? Shouldn't the radiation emitted propagate isotropically in all directions (sphere) instead of anisotropically (cube)? I apologize for the notation; I don't know how to write in latex. Thank you.
 
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the 4 \pi factor can just be folded into the "k" or "G" factor we see in inverse-square laws. either way, they're inverse-square.

but, i agree with your sentiments, which is why i think that more natural Planck Units would be those that normalize 4 \pi G instead of just G and it would be better to choose a natural unit of charge that would normalize \epsilon_0 instead of normalizing 4 \pi \epsilon_0.
 

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