A long wire carries a steady current. When it is bent in a circular form, the magnetic field at its centre is 0.1 T. Now if this wire is bent in a circular loop of 10 turns, what is the magnetic field at its centre?

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(1) 10 T. Given: a wire of fixed length L. Wound as one turn it gives B₁=0.1 T at the centre; it is then rewound as 10 turns. Idea: the field at the centre of a coil is B=(μ₀NI)/(2R), and the same wire wound into more turns has to use a smaller radius. One turn: L=2π R₁. Ten turns: L=10×2π R₂, so R₂=(R₁)/(10). (B₂)/(B₁)=(N₂)/(N₁)×(R₁)/(R₂)=10×10=100. B₂=100×0.1=10 T.

A long wire carries a steady current. When it is bent in a circular form, the magnetic field at its centre is 0.1 T. Now if this wire is bent in a circular loop of 10 turns, what is the magnetic field at its centre?

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