Answer
$\phi=3.62\frac{N.m^2}{C}$
Work Step by Step
We know that:
$\rho=\frac{q}{V}$
This can be rearranged as:
$q=\rho V$
We plug in the known values to obtain:
$q=(500\times 10^{-9})(0.0400)=3.20\times 10^{-11}C$
Now according to Gauss's law
$\phi=\frac{q}{\epsilon_{\circ}}$
We plug in the known values to obtain:
$\phi=\frac{3.20\times 10^{-11}}{8.85\times 10^{-12}}=3.62\frac{N.m^2}{C}$
