Two coaxial long solenoids of equal lengths have currents i 1 and i 2 , the number of turns per unit length n 1 and n 2 and radii r 1 and r 2 r 2 r 1 respectively. If n 1 i 1 = n 2 i 2 and the two solenoids carry currents in the opposite

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Two coaxial long solenoids of equal lengths have currents i 1 and i 2 , the number of turns per unit length n 1 and n 2 and radii r 1 and r 2 r 2 > r 1 respectively. If n 1 i 1 = n 2 i 2 and the two solenoids carry currents in the opposite sense, the magnetic energy stored per unit length is

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Correct answer: A. μ 0 2 n 1 2 i 1 2 π r 2 2 - r 1 2

The magnetic field is non-zero only in the region between the two solenoids, where B = µ 0 n 2 i 2 ∴ Energy stored per unit volume = B 2 2 μ 0 = μ 0 n 2 2 i 2 2 2 The energy per unit length = energy per unit volume × area of cross section where B ≠ 0 = μ 0 n 2 2 i 2 2 2 π r 2 2 - r 1 2 = μ 0 n 1 2 i 1 2 2 π r 2 2 - r 1 2 , since n 1 i 1 = n 2 i 2

Two coaxial long solenoids of equal lengths have currents i 1 and i 2 , the number of turns per unit length n 1 and n 2 and radii r 1 and r 2 r 2 > r 1 respectively. If n 1 i 1 = n 2 i 2 and the two solenoids carry currents in the opposite sense, the magnetic energy stored per unit length is

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