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# A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is $\bigg( \large\frac{\sigma}{2 \in_0} \bigg) \hat n$ , where $\hat n$ is the unit vector in the outward normal direction, and $\sigma$ is the surface charge density near the hole.

Then the field just outside is $(\frac{\sigma}{\in_0}) \hat {n}$ and is zero inside.