The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility $$\chi_{mg} = 1.2 \times 10^{-5}$$) is :

The magnetic field inside a long, closely-wound solenoid is

$$B = \mu H$$

where $$\mu$$ is the permeability of the medium and $$H$$ is the magnetic field strength produced by the current.

In vacuum (or air) $$\mu = \mu_0$$, so the field is

$$B_0 = \mu_0 H$$ $$-(1)$$

When the core is filled by a material of magnetic susceptibility $$\chi$$, its permeability becomes

$$\mu = \mu_0(1 + \chi)$$

Therefore the new magnetic field is

$$B = \mu H = \mu_0(1 + \chi)H$$ $$-(2)$$

Divide $$(2)$$ by $$(1)$$ to find the ratio of the two fields:

$$\frac{B}{B_0} = \frac{\mu_0(1 + \chi)H}{\mu_0 H} = 1 + \chi$$

The fractional (i.e. relative) increase in the field is

$$\frac{B - B_0}{B_0} = (1 + \chi) - 1 = \chi$$

Hence the percentage increase is

$$\chi \times 100\%$$

For magnesium $$\chi_{mg} = 1.2 \times 10^{-5}$$, so

Percentage increase $$= 1.2 \times 10^{-5} \times 100\% = 1.2 \times 10^{-3}\%$$

Option A expresses this value as $$\dfrac{6}{5} \times 10^{-3}\% = 1.2 \times 10^{-3}\%$$, which matches our result.

Therefore, the correct choice is Option A.