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The magnetic field inside a long current-carrying solenoid is 0.6 T. The magnetic energy per unit volume is ______.

Asked in GUJCET 2021 · Energy stored in an inductor

• (1) 1.43×10⁵ J m⁻³
• (2) 5.23×10⁴ J m⁻³
• (3) 2.86×10⁵ J m⁻³
• (4) Zero

Step-by-step solution

Why the other options are wrong

• (2) No single slip gives 5.23×10⁴ J m⁻³. Sanity check: (B²)/(2μ₀) = (0.36)/(2.51×10⁻⁶) ≈ 1.43×10⁵ J m⁻³; 5.23×10⁴ would need a field of only about 0.36 T.
• (3) Drops the 1/2: (B²)/(μ₀) = (0.36)/(4π×10⁻⁷) ≈ 2.86×10⁵ J m⁻³, twice the true energy density.
• (4) A steady field still stores energy. The energy density (B²)/(2μ₀) needs only the field to be present, not changing, so it is non-zero wherever B eq 0.

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