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A circular coil of wire consisting of 100 turns, each of radius 2 cm, carries a current of 0.20 A. The magnetic field at the centre of the coil is ______ T.

Asked in GSEB Board March 2020 · Rotating charges and multiple loops

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

Step-by-step solution

Why the other options are wrong

• (1) π×10⁻⁴ is half the answer — what you get by putting the diameter 4 cm where B=(μ₀NI)/(2R) wants the radius: (μ₀×100×0.2)/(2×0.04)=π×10⁻⁴ T.
• (3) No single slip gives 3π×10⁻⁴: it would need 150 turns, or a radius of 1.33 cm. Sanity check: (μ₀NI)/(2R)=(4π×10⁻⁷×100×0.2)/(0.04)=2π×10⁻⁴ T.
• (4) 10⁻⁴ carries no π. Since μ₀=4π×10⁻⁷ and nothing in (μ₀NI)/(2R) can cancel that π, the answer has to be a multiple of π.

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