A conducting shell, on the inside, is hollow and by using gauss law we calculate the electric field inside the shell. While using gauss law we use flux = charge inside / permittivity of free space = surface integral of $E.dA$ where $E$ is the electric field and $dA$ is the area of the gaussian surface, what confuses me is the fact that there cannot possibly be electric field lines inside the shell as they have nowhere to terminate to, and for integrating E.dA we need cos theta between $E$ and $dA$, so how can we assume that it cannot be zero and land to the conclusion that $E$ must be zeor?
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Inside the shell, you get $$ \int \boldsymbol {E} \cdot d\boldsymbol {A} = 0 $$ Since you can choose the surface arbitrarily, the E field must be zero.
