1. The problem asks about the meaning of the value with units $\mathrm{Nm^2/C^2}$ in Coulomb's law. 2. Coulomb's law describes the force between two point charges. It is given by: $$F = k \frac{|q_1 q_2|}{r^2}$$ where $F$ is the force, $q_1$ and $q_2$ are the charges, $r$ is the distance between them, and $k$ is the Coulomb constant. 3. The value with units $\mathrm{Nm^2/C^2}$ is the Coulomb constant $k$, which quantifies the strength of the electric force in vacuum. 4. Numerically, $k \approx 8.9875 \times 10^9 \ \mathrm{Nm^2/C^2}$. 5. This constant ensures that when you multiply it by the product of charges (in coulombs) and divide by the square of the distance (in meters), the resulting force $F$ is in newtons (N). 6. In summary, the value with units $\mathrm{Nm^2/C^2}$ is the proportionality constant in Coulomb's law that relates electric force to charge and distance.