Answer
$r=27.5 \mathrm{~mm}$
Work Step by Step
To find the one that is less than $R$, we solve
$$
\frac{\mu_0 \varepsilon_0 r}{2} \frac{d E}{d t}\\=\frac{\mu_0 \varepsilon_0 R}{4} \frac{d E}{d t}
$$
for $r$. The result is $r=R / 2=(55.0 \mathrm{~mm}) / 2\\=27.5 \mathrm{~mm}$.
