Two circular coils are made of two identical wires of length 20 cm. One coil has number of turns 9 and the other has 3. If the same current flows through the coils then the ratio of magnetic fields of induction at their centres is

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3 : 1

9 : 1

1 : 9

1 : 3

answer is B.

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Detailed Solution

$\begin{array}{l} l = n \times 2 πr \Rightarrow r \propto \frac{1}{n} \to (1) \\ B = \frac{μ_{0} ni}{2 r} \Rightarrow B \propto \frac{n}{r} \to (2) \end{array}$
from (1) and (2), $B \propto n^{2}$
$\frac{B_{1}}{B_{2}} = \frac{n_{1}^{2}}{n_{2}^{2}} = \frac{9 \times 9}{3 \times 3} = \frac{9}{1}$

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