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There are 50 turns per cm length in a very long solenoid. It carries a current of 2.5 A. The magnetic field at its centre on the axis is ______ T.

Asked in GUJCET 2019 · Solenoid, toroid and field energy

• (1) 5π×10⁻³
• (2) 6π×10⁻³
• (3) 2π×10⁻³
• (4) 4π×10⁻³

Step-by-step solution

Why the other options are wrong

• (2) 6π×10⁻³ would need nI=1.5×10⁴. The stem fixes n=5000 m⁻¹ and I=2.5 A, so nI=1.25×10⁴ and B=5π×10⁻³ T. No single slip lands on this value.
• (3) 2π×10⁻³ is what μ₀nI gives with the turn density taken as 2000 m⁻¹. Fifty turns per centimetre is 50×100=5000 per metre.
• (4) 4π×10⁻³ is the value with the current read as 2 A instead of 2.5 A.

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