To solve this problem, we will use the formula for the magnetic field at the center of a circular coil.$\\$The formula for the magnetic field $B$ at the center of a circular coil is given by:$\\ B = \frac{\mu_0 \cdot N \cdot I}{2R} \\$Where:$\\$• $\mu_0 = 4\pi \times 10^{-7}$ T m/A (permeability of free space)$\\$• $N = 100$ (number of turns)$\\$• $I = 7$ A (current)$\\$• $R = 0.1$ m (radius of the coil, converted from 10 cm)$\\$Substitute the known values into the formula:$\\ B = \frac{4\pi \times 10^{-7} \cdot 100 \cdot 7}{2 \cdot 0.1} \\$Simplify the expression:$\\ B = \frac{4\pi \times 10^{-7} \cdot 700}{0.2} \\ B = \frac{2800\pi \times 10^{-7}}{0.2} \\ B = 14000\pi \times 10^{-7} \\ B = 14\pi \times 10^{-3} \\$Using $\pi \approx 3.14,$ we find:$\\ B \approx 14 \times 3.14 \times 10^{-3} \\ B \approx 43.96 \times 10^{-3} \\ B \approx 44$ mT$\\$Therefore, the magnitude of the magnetic field at the center of the coil is approximately $44$ mT.$\\$This corresponds to Option 3.