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We solve exactly the dielectric response of a non-insulating sphere of radius$a$ suspended in symmetric, univalent electrolyte solution, withideally-polarizable interface but without significant $\zeta$-potential. Wethen use this solution to derive the dielectric response of a dilute randomsuspension of such spheres, with volume fraction $f\ll1$, within theMaxwell-Garnett Effective Medium Approximation. Surprisingly, we discover ahuge dielectric enhancement in this bare essential model of dielectricresponses 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 effectivedielectric 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 diffusioncoefficient. As $\lambda$ is of the order nm even for dilute electrolytesolution, even for sub-mm spheres and low volume fraction $f=0.05$ the hugegeometric 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 themixture, which is usually negligible in pure electrolyte solution. The phaseshift 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 aphysical picture of the enhancement from an accumulation of charges in a thinExternally Induced Double Layer (EIDL) due to the blocking boundary conditionson interfaces.

Dielectric Enhancement from Non-Insulating Particles with Ideally Polarized Interfaces and Zero $\zeta$-Potential I: Exact Solution