An arrangement with a pair of quarter circular coils of radii $r$ and $R$ with a common centre $C$ and carrying a current $I$ is shown in the figure. The permeability of free space is $\mu_0$. The magnetic field at $C$ is
KVPY 2013, Medium
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(b)
Magnetic field at $C$ is resultant field due to arcs of radius $R$ and $r$.
$\therefore \quad B =\frac{1}{4}\left(\frac{\mu_{0} I}{2 r}\right) \odot-\frac{1}{4}\left(\frac{\mu_{0} I}{2 R}\right) \otimes$
$=\frac{1}{8} \cdot \mu_0 I\left(\frac{1}{r}-\frac{1}{R}\right) \odot$
Net field is out of the plane of paper.
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