= Solution
In the midplane, the vacuum <magnetic dipole field> has scale $B_0\sim\mu/r^3$, while the result of part i gives $j\sim\Omega^2\mu/(cr^2)$. <Ampère's law> then gives the induced-field estimate
$$
\frac{B_i}{r}\sim\frac{j}{c},
\qquad
B_i\sim\frac{\Omega^2\mu}{c^2r},
$$
where numerical factors are immaterial in this <dimensional analysis>. Thus $B_i\sim B_0$ at
$$
\boxed{R_e\sim\frac c\Omega}.
$$
This is the <light cylinder radius>: rigid corotation would have $u=\Omega R_e\sim c$. The nonrelativistic approximation and the assumed unmodified vacuum field therefore fail at the same scale, and a self-consistent <pulsar magnetosphere> must replace them.
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