A wire of length 314 cm carrying current of 14 A is bent to form a circle. The magnetic moment of the coil is ________ A -m². [Given π=3.14]

Solution

Physics sir · 3 steps

The wire's length becomes the circle's circumference, so find the radius first, then the area.

1. Length to radius. The whole wire wraps once around the circle, so 2π r = 3.14 m. With π = 3.14, this gives r = 3.14/(2 × 3.14) = 0.5 m.
2. Area of loop. A = π r² = 3.14 × (0.5)² = 0.785 m².

   m = IA = 14 × 0.785 = 10.99 A m²

3. So. The magnetic moment is 10.99 A m², which rounds to 11.

The common slip: 44. Taking L/π = 1 m as the radius instead of the diameter gives A = 3.14 m² and m ≈ 44.

The idea to keep. When a wire of length L is bent into one circular loop, m = IA = IL²/4π. Convert the length to metres before you start.

Answer from the NTA final answer key. Solution by PrepWiser.