Use Gauss’s Law to prove that the electric field anywhere inside the hollow of a charged spherical shell must be zero.
My attempt:
$$\int \mathbf{E}\cdot \mathbf{dA} = \frac{q_{net}}{e}$$
$$\int E \ dAcos\theta = \frac{q_{net}}{e}$$
$$E \int dA = \frac{q_{net}}{e}$$
$E\ 4\pi r^2 = \frac{q_{net}}{e}$ and since it is a hollow of a charged spherical shell the $q_{net}$ or $q_{in}$ is $0$ so: $E = 0$.
Is my reasoning on this problem correct? Essentially $E$ is $0$ because there is no charge enclosed.