= Longitudinal capacitor field under a normal boost
For ideal oppositely charged parallel plates, the normal <electric field> is $\sigma/\epsilon_0$. A boost along that normal leaves each transverse plate area unchanged. Invariance of total charge therefore preserves <surface charge density> and the normal <electric field>. The plate separation contracts, but the large-plate field does not depend on that separation. Including longitudinal contraction in a <voltage> argument while holding <voltage> fixed would impose an unsupported extra assumption.
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