A long thin non-conducting cylindrical pipe of radius $R$ carrying a uniform surface charge density $σ$ is rotating about its axis with a constant angular speed $ω$ . The energy density of the magnetic field inside the tube is

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The rotating cylinder is equivalent to a solenoid with current per unit length = σ ω R ∴ B = μ 0 σ ω R ∴ u = 1 2 μ 0 B 2 = 1 2 μ 0 μ 0 2 · σ ω R 2 u = μ 0 σ 2 ω 2 R 2 2

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JEE Main 2027 (Class 12)