Final answer:
The ratio of the magnetic fields along two toroids carrying the same current is determined using the B-field formula for a toroid. Upon calculation with given parameters for each toroid, the ratio is found to be 2:1. Therefore, the correct option is C.
Step-by-step explanation:
To determine the ratio of the magnetic fields along the two toroids that carry the same current, we use the formula for the magnetic field inside a toroid, which is B = μ_0 • (N • I) / (2 • π • r), where μ_0 is the permeability of free space, N is the number of turns, I is the current, and r is the average radius of the toroid.
For toroid 1 with 200 turns and a radius of 40 cm, B1 = μ_0 • (200 • I) / (2 • π• 40). For toroid 2 with 100 turns and a radius of 20 cm, B2 = μ_0 • (100 • I) / (2 • π• 20). Simplifying, we get B1/B2 = (200/40) / (100/20), which simplifies further to 2:1. Therefore, the ratio of the magnetic fields along the two loops is 2:1.