# Is there no electric field inside a hollow cylinder?

This is from question 4 here:

The question discusses a hollow conducting cylinder with a charge $\lambda$ per unit area and radius $a$. (It also mentions another surrounding cylinder, but that's not relevant to my question.) It asks for the field for all radius $r$. Now for $r<a$ the answer says there is no field ($E=0$). Now it makes sense to me that since there is no charge inside the hollow cylinder, there will be no field radiating outward, but won't there still be a field inside the cylinder everywhere except the exact center that would drive a test charge toward the center of the cylinder?

The answer seems to me to read that a test charge placed inside the cylinder would not experience any force, but this does not make sense to me. Am I missing something?