A long solenoid is completely filled with a core material. The...

The ratio of induced magnetization $M$ to magnetic intensity $H$ is the magnetic susceptibility $\chi_m$ of the material.

$\chi_m = \dfrac{M}{H} = 0.025$

The relative permeability of the core material is given by:

$\mu_r = 1 + \chi_m$

The magnetic field inside the solenoid with the core is $B = \mu_r B_0$, where $B_0$ is the magnetic field without the core.

The percentage increase in the magnetic field is:

$\dfrac{B - B_0}{B_0} \times 100\% = (\mu_r - 1) \times 100\% = \chi_m \times 100\%$

Percentage increase $= 0.025 \times 100\% = 2.5\%$

Answer: $2.5\%$