Question

Two toroids 1 and 2 have total number of turns 200 and 100 respectively with average radii 40cm and 20cm respectively. If they carry same current i, the ratio of the magnetic fields along the two loops is

(a) 1:1
(b) 4:1
(c) 2:1
(d) 1:2

Answer 1

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.