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In our physics class we were discussing about Coulomb's Law and equation for the electrostatic force between two points: $$F_{e}=\frac{Q_{1}Q_{2}}{4\pi \epsilon_0 r^2}$$

From the equation a query arose which is for what reason does the constant involve $4\pi$.

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  • $\begingroup$ The link I've suggested has itself been closed as a duplicate of a couple of other questions. However I think it is the best match to your question and the answers to it are relevant. $\endgroup$
    – John Rennie
    Dec 31, 2014 at 10:05

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It's just a matter of rationalisation and mathematical convenience. $4\pi$ corresponds to the whole solid angle, which usually simplifies when you deal with Gauss' theorem. In other words, you can simply redefine a constant $k$ to be any multiple of another constant, $1/E_0$ in this case.

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    $\begingroup$ Can you explain it more explicitly with some kind of equations or diagrams.I understand calculus but I am new to Electricity & Magnetism. $\endgroup$
    – Devarsh Ruparelia
    Dec 31, 2014 at 10:00
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    $\begingroup$ Following John Rennie's suggestion, here is a relevant link on SE physics.stackexchange.com/q/74254 $\endgroup$
    – Phoenix87
    Dec 31, 2014 at 10:08

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