Two long straight solenoids, S₁ and S₂ , are constructed such that S₁ has length L , total turns N , and carries a current I . Solenoid S₂ has length 2L , total turns 3N , and carries a current I 2 . The ratio of the magnetic field at the centre of S₁ to that at the centre of S₂ is:

Step-by-step solution

The magnetic field at the centre of a long solenoid is given by B = ₀ n I , where n = N L is the number of turns per unit length. For solenoid S₁ : B₁ = ₀ ( N L ) I For solenoid S₂ : Length = 2L , Total turns = 3N , Current = I 2 B₂ = ₀ ( 3N 2L ) ( I 2 ) B₂ = 3 4 ₀ ( N L ) I Taking the ratio of B₁ to B₂ : B₁ B₂ = ₀ ( N L ) I 3 4 ₀ ( N L ) I = 1 3 4 = 4 3 Therefore, the ratio is 4 : 3 . Answer: 4 : 3