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Question:

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field B1 at its centre when a current I passes through it. The second wire is bent into a coil with three identical loops adjacent to each other and produces magnetic field B2 at the centre of the loops when current I passes through it. The ratio B1:B2 is:

1:1

1:9

9:1

1:3

Solution:

Magnetic field due to the first loop ,B1=μ₀I/2r
For 2nd wire, there are three loops (n=3) so total current enclosed by the loops ,Ien=I/3+I/3+I/3=I
Radius of second loop=r/3 because the original wires are identical.
magnetic field B2=μ₀Ien/2(r/3) = μ₀3I/2r
B1/B2=1/3