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There are 100 turns per cm length in a very long solenoid. It carries a current of 5 A. The magnetic field at its centre on the axis is ______ T.

Asked in GSEB Board July 2015 · Solenoid, toroid and field energy

• (1) 3.14×10⁻²
• (2) 6.28×10⁻²
• (3) 9.42×10⁻²
• (4) 12.56×10⁻²

Step-by-step solution

Why the other options are wrong

• (1) (μ₀ nI)/2 is the field at the END of a long solenoid, where the turns lie on one side only. At the centre the full μ₀ nI applies.
• (3) Half as much again as the answer: it needs n=1.5×10⁴ m⁻¹, that is 150 turns per cm. The stem gives 100 per cm.
• (4) Twice the answer: it needs n=2×10⁴ m⁻¹ (200 turns per cm) or a current of 10 A.

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