Two wires A and B are of lengths 40 cm and 30 cm. A is bent into a circle of radius r and B into an arc of radius r. A current i₁ is passed through A and i₂through B. To have the same magnetic induction at the centre, the ratio of i₁ : i₂ is

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3 : 5

3 : 4

2 : 3

4 : 3

answer is A.

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Detailed Solution

$\begin{array}{l} B_{1} = \frac{μ_{0} i_{1}}{4 πr} θ_{1} = \frac{μ_{0} i_{1}}{4 πr} \frac{40}{r}; B_{2} = \frac{μ_{0} i_{2}}{4 πr} \frac{30}{r} \\ B_{1} = B_{2}; 4 i_{1} = 3 i_{2}; \frac{i_{1}}{i_{2}} = \frac{3}{4} \end{array}$

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