Two long solenoids X and Y have equal areas, equal relative permeability, but the length of X is twice that of Y and the number of turns per unit length of X is half that of Y. Find Lₓ : Lᵧ.
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Two long solenoids X and Y have equal areas, equal relative permeability, but the length of X is twice that of Y and the number of turns per unit length of X is half that of Y. Find Lₓ : Lᵧ.

G1 Physics · Accepted Answer

Step 1: Self-inductance of a long solenoid is L = μ₀μᵣ(N²A/ℓ) = μ₀μᵣn²Aℓ. Step 2: For two solenoids of same material and area, L ∝ n²ℓ. Step 3: If nₓ = nᵧ/2 and ℓₓ = 2ℓᵧ, then Lₓ/Lᵧ = (1/2)²×2 = 1/2. Answer A (1:2). Final answer: (C) 8 : 1.