A current of 2 A flows in a solenoid 0.5 m long with a radius of 1 cm and 500 turns (treat it as sufficiently long). Which is closest to the magnetic flux density near the center inside it? (In vacuum, μ0 = 4π×10⁻⁷ H/m.)

Answer: B. About 2.5 mT

Applying Ampère's law to a solenoid, the interior field is nearly uniform with B = μ0nI (n: turns per unit length). Since n = 500/0.5 m = 1000 m⁻¹, B = 4π×10⁻⁷ × 1000 × 2 ≈ 2.51×10⁻³ T ≈ 2.5 mT. Inside a sufficiently long solenoid the flux density does not depend on the radius, and the field outside can be taken as nearly zero. Inserting an iron core multiplies the flux density by the relative permeability, as long as the core does not saturate.

• A. About 1.3 mT uses the total turns, 500, instead of the turns per unit length n.
• B. Correct. μ0 × 1000 m⁻¹ × 2 A ≈ 2.5 mT.
• C. About 40 µT puts the 1 cm radius into the straight-wire formula μ0I/(2πr), ignoring the turns.