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The self-inductance of a long solenoid of length ℓ, area A, with n turns per unit length is approximately:
AL = μ₀ n² A ℓ
BL = μ₀ n A / ℓ
CL = μ₀ n² / (A ℓ)
DL = μ₀ n A ℓ
Answer & Solution
Correct answer: A. L = μ₀ n² A ℓ
1. Total turns N = n ℓ; flux per turn Φ₁ = B A = (μ₀ n I) A.
2. Total flux linkage Λ = N Φ₁ = (n ℓ)(μ₀ n I A) = μ₀ n² ℓ A I.
3. So L = Λ / I = μ₀ n² A ℓ.
_Source: NCERT Class 12 Physics Ch 6 §6.8 Self-Inductance of a Solenoid_
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