## College Physics (4th Edition)

(a) $\Phi = E~(4\pi~r^2)$ (b) $c = \frac{1}{\epsilon_0}$
(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 $c$: $\Phi = c~q$ $E~(4\pi~r^2) = c~q$ $\frac{4\pi~r^2~q}{4\pi~\epsilon_0~r^2} = c~q$ $\frac{q}{\epsilon_0} = c~q$ $c = \frac{1}{\epsilon_0}$