1. Given data

   • Length of wire: $314\text{ cm} = 3.14\text{ m}$
   • Current: $I = 14\text{ A}$
   • The wire is bent into a circle.

2. Find the radius of the circle The length of the wire becomes the circumference: $2\pi r = 3.14$ Using $\pi = 3.14$, $2(3.14)r = 3.14$ $6.28r = 3.14$ $r = \frac{3.14}{6.28} = 0.5\text{ m}$

3. Find the area of the circular loop $A = \pi r^2$ $A = 3.14 \times (0.5)^2$ $A = 3.14 \times 0.25 = 0.785\text{ m}^2$

4. Magnetic moment of the coil For a single circular loop, $m = IA$ $m = 14 \times 0.785$ $m = 10.99 \text{ A-m}^2$

5. Integer answer $m \approx 11 \text{ A-m}^2$

Therefore, the required integer answer is 11.