If the electric flux entering and leaving a closed surface are $\phi_1$ and $\phi_2$ S.I units respe

Question

If the electric flux entering and leaving a closed surface are $\phi_1$ and $\phi_2$ S.I units respectively, then the charge inside the surface of permittivity of free space $\epsilon_0$ is

Professor PC Thomas Classes · Answer

According to Gauss's law, $q = \epsilon_0 \phi_{net}$ where $\phi_{net}$ is the net outward flux. Net outward flux = flux leaving - flux entering = $\phi_2 - \phi_1$. Therefore, $q = \epsilon_0(\phi_2-\phi_1)$ or $q = \frac{\phi_2-\phi_1}{\epsilon_0}$.