A length $L$ of wire carries a steady current $I$ . It is bent first to form a circular plane coil of one turn. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre caused by the same current is

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four times of its first value

a half of its first value

unaltered

a quarter of its first value

answer is C.

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Detailed Solution

If $R$ and $r$ are the radius of bigger and smaller loop respectively, then $2 πR = 2 \times 2 π r, o r r = \frac{R}{2}$ .

$B_{1} = \frac{μ_{0} i}{2 R} a n d B_{2} = \frac{μ_{0} (2) i}{2 r} = \frac{μ_{0} (2) i}{2 \frac{R}{2}} = 4 B_{1}$

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