= Solution
For $b<r<a$, a coaxial <Gauss surface> of length $l$ encloses net charge $Q$: the sphere and the cavity-wall charge cancel, leaving $+Q$ on the outside of the inner conductor. In the long-cylinder approximation,
$$
E_r(r)\,2\pi rl=\frac Q{\epsilon_0},\qquad
\boxed{E_r(r)=\frac{Q}{2\pi\epsilon_0lr}=\frac{2RV}{lr}.}
$$
The <electric field> points radially outward for $V>0$. End effects and axial nonuniformity near the openings are excluded by the ideal <coaxial cylindrical capacitor> approximation.
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