PX157 - B6c - faraday cage

a person inside a conducting shell (faraday cage) in a uniform electric field in $\hat{z}$
applying PX157 - B5a - gauss's law:

\begin{aligned} \subset \supset \iint_{S} \vec{E} d \vec{S} & = \frac{Q_{e n c l .}}{ϵ_{0}} \\ E_{0} \hat{z} \cdot \hat{r} d S & = \frac{σ}{ϵ_{0}} d S \\ σ & = ϵ_{0} E_{0} \cos θ \end{aligned}