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(B) Gauss's law is a consequence of the inverse square law of electrostatics.According to Gauss's law,the total electric flux $\phi$ through a closed

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$r^{-2}$

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(B) Gauss's law is a consequence of the inverse square law of electrostatics.According to Gauss's law,the total electric flux $\phi$ through a closed surface is given by $\phi = \frac{q}{\epsilon_0}$.For a point charge $q$,the electric field $E$ at a distance $r$ is $E = \frac{1}{4 \pi \epsilon_0} \frac{q}{r^2}$.The electric flux $\phi$ is defined as $\phi = \oint E \cdot dA = E \cdot A$,where $A$ is the surface area of a sphere of radius $r$,which is $4 \pi r^2$.Substituting $E$ and $A$,we get $\phi = (\frac{1}{4 \pi \epsilon_0} \frac{q}{r^2}) 	imes (4 \pi r^2) = \frac{q}{\epsilon_0}$.Since the force $F$ between two charges is given by Coulomb's law as $F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2}$,it is clear that $F \propto r^{-2}$.Thus,Gauss's law holds true only if the force varies as $r^{-2}$.

Gauss's law is true only if the force due to a charge varies as:

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