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Offline Centres

In the loops shown in below Figure, all curved sections are either semicircles or quarter circles. All the loops carry same current. The magnetic fields at the centers have magnitudes B₁, B₂,B₃ and B₄. Then,

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$B_{4}$ is maximum

B₁ > B₄ > B₃ > B₂

B₄ > B₁ > B₂ > B₃

B₃ is minimum

answer is A, B, D.

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Detailed Solution

$B_{1} = \frac{μ_{0} i}{4} (\frac{1}{b} + \frac{1}{a}), B_{2} = \frac{μ_{0} i}{4} (\frac{1}{b} - \frac{1}{a}), B_{3} < \frac{μ_{0} i}{4} (\frac{1}{b} - \frac{1}{a}) a n d B_{4} > \frac{μ_{0} i}{4} (\frac{1}{b} - \frac{1}{a})$

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

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