Solution
= Solution
The uniform <charge density> is $\rho_e=3Q/(4\pi R^3)$. Spherical symmetry makes the <electric field> radial and constant in magnitude on each concentric sphere. A sphere of radius $r<R$ encloses charge $Q(r/R)^3$. <Gauss's law> therefore gives $4\pi r^2E_r=Qr^3/(\varepsilon_0R^3)$, so
$$
\boxed{\mathbf E(\mathbf r)=\frac{Q}{4\pi\varepsilon_0R^3}\mathbf r,\qquad |\mathbf r|<R.}
$$
This also defines the zero <electric field> at the centre by continuity.