Given: $n = 500$, $R = 0.05$ m, $I = 7$ A, $x = 0.12$ m.

(A) At axial point:
$$B_{axis} = \frac{\mu_0 n I R^2}{2(R^2 + x^2)^{3/2}}$$
$$R^2 + x^2 = (0.05)^2 + (0.12)^2 = 0.0025 + 0.0144 = 0.0169$$
$$(R^2 + x^2)^{3/2} = (0.0169)^{3/2} = 0.13^3 = 2.197 \times 10^{-3}$$
$$B_{axis} = \frac{4\pi \times 10^{-7} \times 500 \times 7 \times 0.0025}{2 \times 2.197 \times 10^{-3}} = \frac{4\pi \times 10^{-7} \times 8.75}{4.394 \times 10^{-3}}$$
$$B_{axis} \approx 2.49 \times 10^{-3} \text{ T}$$

(B) At centre ($x = 0$):
$$B_{centre} = \frac{\mu_0 nI}{2R} = \frac{4\pi \times 10^{-7} \times 500 \times 7}{2 \times 0.05} = \frac{4\pi \times 10^{-7} \times 3500}{0.1}$$
$$B_{centre} = 4\pi \times 3.5 \times 10^{-3} = 4.4 \times 10^{-2} \text{ T}$$