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Two coaxial long solenoids of equal length have inner radius r1 = 3 m and outer radius r2 = 5 m. Their ampere-turns per unit length satisfy n1*i1 = n2*i2 = 250 A/m and they carry currents in opposite senses. Find the magnetic energy stored per unit length in SI units. [Use mu0 = 4*pi*10⁻⁷ H/m and pi² = 10]

1. 1 J/m
2. 2 J/m
3. 4 J/m
4. pi J/m

Correct answer: 2 J/m

Solution

Inside the inner solenoid the two opposite fields cancel. In the annular region B = mu0*250. Energy per unit length = mu0*250²/2 * pi*(25-9) = mu0*31250*16*pi = 2 J/m using pi² = 10.

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