Answer
The electric field at $r = \frac{a}{2.00}$ is zero.
Work Step by Step
We can draw a Gaussian sphere of radius $r = \frac{a}{2.00}$ that is concentric with the spherical shell.
The enclosed charge within this sphere is zero.
Therefore, the flux through the surface of the sphere is zero.
It follows that the electric field at $r = \frac{a}{2.00}$ is zero.
