At the centre of a long solenoid carrying a current of 2.0 A , the...

The magnetic intensity $H$ inside a long solenoid is given by the formula $H = nI$, where $n$ is the number of turns per unit length and $I$ is the current flowing through the solenoid.

The value of magnetic intensity $H$ depends only on the free current $I$ and the geometry of the solenoid ($n$). It is completely independent of the medium or the material of the core inserted inside the solenoid.

Since the current and the number of turns per unit length remain unchanged, the magnetic intensity $H$ will remain the same after the rod is inserted.

Thus, the magnetic intensity $H = 1500 \text{ A m}^{-1}$.