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

Step-by-step solution

The magnetic field within the turns of toroid is B = ₀ NI 2 r where, N = number of turns, I = current in loops and r = radius of each turn Here, N ₁=200, ~N ₂=100, r ₁=40 ~cm , r ₂=20 ~cm and current I is same, then B ₁ ~B ₂ = ₀ ~N ₁ I 2 r ₁ 2 r ₂ ₀ ~N ₂ I Substituting the given values in the above relation, we get aligned B ₁ ~B ₂ & = ( N ₁ ~N ₂ ) ( r ₂ r ₁ ) & = ( 200 100 ) ( 20 40 )=2 1 2 =1 B ₁: B ₂ & =1: 1 aligned