  We solve exactly the dielectric response of a non-insulating sphere of radius
$a$ suspended in symmetric, univalent electrolyte solution, with
ideally-polarizable interface but without significant $\zeta$-potential. We
then use this solution to derive the dielectric response of a dilute random
suspension of such spheres, with volume fraction $f\ll1$, within the
Maxwell-Garnett Effective Medium Approximation. Surprisingly, we discover a
huge dielectric enhancement in this bare essential model of dielectric
responses of solids in electrolyte solution: at low frequency $\omega\tau_D \ll
(\lambda/a) / (\sigma_w / \sigma_s+1/2)$, the real part of the effective
dielectric constant of the mixture is $1-(3f/2)+(9f/4)(a/\lambda)$. Here
$\sigma_{w/s}$ is the conductivity of the electrolyte solution/solids,
$\lambda$ is the Debye screening length in the solution, $\tau_D=\lambda^2/D$
is the standard time scale of diffusion and $D$ is the ion diffusion
coefficient. As $\lambda$ is of the order nm even for dilute electrolyte
solution, even for sub-mm spheres and low volume fraction $f=0.05$ the huge
geometric factor $a/\lambda$ implies an over $10^4$-fold enhancement.
Furthermore, we show that this enhancement produces a significant low frequency
($\omega\tau_D\ll1$) phase shift $\tan\theta = \mathrm{Re}~ \epsilon(\omega) /
\mathrm{Im} ~\epsilon(\omega)$ in a simple impedance measurement of the
mixture, which is usually negligible in pure electrolyte solution. The phase
shift has a scale-invariant maximum
$\tan\theta_{\mathrm{max}}=(9/4)f/(2\sigma_w/\sigma_s+1)$ at
$\omega_{\mathrm{max}}=(2D/\lambda a)/(2\sigma_w/\sigma_s+1)$. We provide a
physical picture of the enhancement from an accumulation of charges in a thin
Externally Induced Double Layer (EIDL) due to the blocking boundary conditions
on interfaces.
