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Offline Centres

In the loop shown, all curved sections are either semicircles or quarter circles. All loops carry the same current. The magnetic field at the centres have magnitudes $B_{1}, B_{2}, B_{3}$ and $B_{4}$
(i) $B_{4}$ is maximum (ii) $B_{3}$ is minimum
$(i i i) B_{4} > B_{1} > B_{2} > B_{3}$ $(i v) B_{1} > B_{4} > B_{3} > B_{2}$

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$i, i i, i i i$

$i i, i i i$

$i, i i$

$i i, i v$

answer is A.

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Detailed Solution

$B_{1} = \frac{μ_{0} I}{4 a} + \frac{μ_{0} I}{4 b} = \frac{μ_{0} I}{4 a} + \frac{μ_{0} I}{8 b} + \frac{μ_{0} I}{8 b}$

$B_{4} = \frac{μ_{0} I}{4 a} + \frac{μ_{0} I}{8 b} + \frac{μ_{0} I}{8 c}, c > b$

$B_{4} > B_{1}$

$B_{2} = \frac{μ_{0} I}{4 b} - \frac{μ_{0} I}{4 a} = \frac{μ_{0} I}{8 b} + \frac{μ_{0} I}{8 b} - \frac{μ_{0} I}{4 a}$

$B_{3} = \frac{μ_{0} I}{8 b} + \frac{μ_{0} I}{8 d} - \frac{μ_{0} I}{4 a}, d > b$

$B_{2} > B_{3}$

$B_{4} > B_{1} > B_{2} > B_{3}$

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