Answer
(a) $\Phi = E~(4\pi~r^2)$
(b) $c = \frac{1}{\epsilon_0}$
Work Step by Step
(a) We can find an expression for the electric flux:
$\Phi = E \cdot A = E~(4\pi~r^2)$
(b) Note that $~E = \frac{q}{4\pi~\epsilon_0~r^2}$
We can find the constant of proportionality $c$:
$\Phi = c~q$
$E~(4\pi~r^2) = c~q$
$\frac{4\pi~r^2~q}{4\pi~\epsilon_0~r^2} = c~q$
$\frac{q}{\epsilon_0} = c~q$
$c = \frac{1}{\epsilon_0}$
