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Obtain Coulomb's law from Gauss's law....

Obtain Coulomb's law from Gauss's law.

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As shown in figure, consider a point charge +q kept at O.
A Gaussian surface .S. is shown in figure includes charge q.
Consider surface area `vecds` at point E Here, `vecE || vecds` ds and so that `theta =0^(@)` .
According to Gauss.s law,
`phi =q/epsilon_(0)`
`therefore int vecE.vec(ds) = q/epsilon_(0)`
`therefore intE.ds cos0^(@) =q/epsilon_(0)[therefore vecE || vecds]`
`therefore E=q/(4piepsilon_(0)r^(2))`
`therefore F/q =q/(4piepsilon_(0)r^(2))`
`therefore F = (Kq.q_(0))/r^(2)`
This is Coulomb.s law.
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