To solve this problem, we need to calculate the magnetic field strength at the center of a long solenoid.$\\$The formula for the magnetic field inside a long solenoid is given by:$\\ B = \mu_0 \cdot n \cdot I \\$Where:$\\$• $B$ is the magnetic field strength.$\\$• $\mu_0 = 4\pi \times 10^{-7} \,$T m/A$$ is the permeability of free space.$\\$• $n$ is the number of turns per unit length.$\\$• $I$ is the current flowing through the solenoid.$\\$Given:$\\$• Radius of the solenoid $= 1 \,$mm (not needed for the calculation as the field is uniform inside).$\\$• Number of turns per mm $= 100 \,$turns/mm.$\\$• Current $I = 1 \,$A.$\\$First, convert the number of turns per mm to turns per meter:$\\ n = 100 \,$turns/mm$= 100 \times 1000 \,$turns/m$= 100000 \,$turns/m$\\$Now, substitute the values into the formula:$\\ B = (4\pi \times 10^{-7}) \cdot 100000 \cdot 1 \\$Calculate:$\\ B = 4\pi \times 10^{-7} \times 100000 \\ B = 4\pi \times 10^{-2} \\$Using $\pi \approx 3.14,$ we find:$\\ B = 4 \times 3.14 \times 10^{-2} \\ B = 12.56 \times 10^{-2} \,$T$\\$Therefore, the magnetic field strength at the center of the solenoid is $12.56 \times 10^{-2} \,$T$. \\$This corresponds to Option 2.