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A solenoid of length 0.5 m has a radius of 1 cm and is made up of 500 turns. If the magnitude of the magnetic field inside the solenoid is 6.28×10⁻³ T, then it carries a current of ______ A.

Asked in GSEB Board July 2021 · Solenoid, toroid and field energy

• (1) 4
• (2) 5
• (3) 2
• (4) 10

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 4 A. Sanity check: n=(500)/(0.5)=1000 m⁻¹, so I=B/(μ₀n)=(6.28×10⁻³)/(4π×10⁻⁷×1000)=5 A.
• (3) 2 A would need a turn density of 2500 m⁻¹. This solenoid has (500)/(0.5)=1000 turns per metre.
• (4) 10 A comes from using the 500 turns as the turn density instead of dividing by the length: (6.28×10⁻³)/(4π×10⁻⁷×500)=10 A.

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