The magnetic susceptibility ($$\chi_m$$) of a material is the measure of how much the material becomes magnetized in response to an external magnetic field. When the material is placed in a magnetic field, the net magnetic field ($$B$$) inside the material is the sum of the external magnetic field ($$B_0$$) and the field produced by the material itself ($$B_{material}$$). This relationship can be expressed as :

$$B = B_0 + B_{material}$$

Magnetic susceptibility is related to the relative permeability ($$\mu_r$$) of the material :

$$\mu_r = 1 + \chi_m$$

The magnetic field inside the toroid can be calculated using the following formula :

$$B = \mu_0 \mu_r H$$

where $$\mu_0$$ is the permeability of free space, $$\mu_r$$ is the relative permeability of the material, and $$H$$ is the magnetic field strength.

Now, let's consider the percentage increase in the magnetic field when the material is placed inside the toroid. The initial magnetic field ($$B_0$$) is given by :

$$B_0 = \mu_0 H$$

After the material is placed inside the toroid, the magnetic field becomes :

$$B = \mu_0 \mu_r H = \mu_0 (1 + \chi_m) H$$

The percentage increase in the magnetic field can be calculated as :

$$\frac{B - B_0}{B_0} \times 100\% = \frac{\mu_0 (1 + \chi_m) H - \mu_0 H}{\mu_0 H} \times 100\%$$

Substitute the value of $$\chi_m = 2 \times 10^{-2}$$ :

$$\frac{B - B_0}{B_0} \times 100\% = \frac{(1 + 2 \times 10^{-2}) - 1}{1} \times 100\% = 2\%$$

Thus, the percentage increase in the value of the magnetic field inside the toroid is 2%.