Two long coaxial solenoids S1 and S2 of equal length l have radii r1 and r2 (with r1 < r2) and turns per unit length n1 and n2 respectively. What is their mutual inductance M per unit length in vacuum?

Answer and explanation

Correct answer: C. μ₀ n₁ n₂ π r₁²

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  1. Step 1: When current flows through the outer solenoid , it produces a uniform axial magnetic field inside it: .
  2. Step 2: This magnetic field passes through the inner solenoid of cross-sectional area .
  3. Step 3: The total magnetic flux linked with solenoid having turns is:
  4. Step 4: By definition, mutual inductance is .
  5. Step 5: Dividing by length , the mutual inductance per unit length is: .
Answer
μ₀ n₁ n₂ π r₁²
Why not the others: 'μ₀ n₁ n₂ π r₂²' uses the outer radius , but the inner solenoid cannot capture magnetic flux outside its own area ; 'μ₀ (n₁ + n₂) π r₁²' adds the turns per unit length rather than multiplying them; 'μ₀ n₁ n₂ π * (r₂² - r₁²)' uses the annular area between the two solenoids.

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