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Consider a uniform plane wave with amplitude $(E_0)$ of $10 \: V/m$ and $1.1$ GHz frequency travelling in air, and incident normally on a dielectric medium with complex relative permittivity $(\varepsilon _r)$ and permeability $(\mu _r)$ as shown in the figure.

The magnitude of the transmitted electric field component (in V/m) after it has travelled a distance of $10$ cm inside the dielectric region is ____________.