When a certain material is inserted into the empty space of a...

The percentage increase in the magnetic field is given by:
$\Delta B (\%) = \dfrac{B_{\text{new}} - B_{\text{old}}}{B_{\text{old}}} \times 100\%$

Since $B_{\text{old}} = \mu_0 n i$ and $B_{\text{new}} = \mu n i = \mu_r \mu_0 n i$, we have:
$\Delta B (\%) = \dfrac{\mu_r \mu_0 n i - \mu_0 n i}{\mu_0 n i} \times 100\% = (\mu_r - 1) \times 100\%$

We know that $\mu_r - 1 = \chi$, where $\chi$ is the magnetic susceptibility.
Given that the percentage increase is $0.0025\%$ :
$\chi \times 100 = 0.0025$
$\chi = \dfrac{0.0025}{100} = 2.5 \times 10^{-5}$

The relative permeability $\mu_r$ is:
$\mu_r = 1 + \chi = 1 + 0.000025 = 1.000025$

Answer: $1.000025$