= Solution
The <electric field> magnitude falls as $1/r^2$ throughout the vacuum gap, so its maximum occurs just outside the inner sphere:
$$
E_{\max}=\frac{|V_1|b}{a(b-a)}=\frac{10^3\times0.4}{0.1(0.4-0.1)}.
$$
Thus
$$
\boxed{E_{\max}=1.333\times10^4\ \mathrm{V\,m^{-1}},\qquad r=a^+}.
$$
Inside the metal the <electric field> is zero. The one-sided gap value is the relevant value for dielectric breakdown; the ideal zero-thickness conducting boundary itself should not be assigned a single field value across its surface-charge discontinuity.
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