Consider the circular loop having current $i$ and with central point $O$. The magnetic field at the central point $O$ is
AIIMS 2015, Diffcult
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(b)
Magnetic field at the center due to the inner loop of radius $R=\frac{3}{4} \times \frac{\mu_0 I}{2 R}$ downwards
Magnetic field at the center due to the outer loop of radius $3 R=\frac{1}{4} \times \frac{\mu_0 I}{2(3 R)}$ downwards
Magnetic field at center due to the two straight wire segments is zero.
Hence net magnetic field at center of loop $=\frac{3 \mu_0 I}{8 R}+\frac{\mu_0 I}{24 R}$ downwards $=\frac{5 \mu_0 I}{12 R}$ downwards
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