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  4. Two concentric circular loops of radii R and 2R carry currents of 2I and I respectively in opposite sense (ie, clockwise in one coil and counter-clockwise in the other coil). The resultant magnetic field at their common centre is

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Q. Two concentric circular loops of radii $R$ and $2R$ carry currents of $2I$ and $I$ respectively in opposite sense (ie, clockwise in one coil and counter-clockwise in the other coil). The resultant magnetic field at their common centre is

J & K CETJ & K CET 2010Moving Charges and Magnetism

Solution:

$B_{1}=\frac{\mu_{0} \times 2 i}{2 \times R}$
Similarly, $B_{2}=\frac{\mu_{0} i}{4 R}$
$B_{net}=\frac{\mu_{0} i}{R}-\frac{\mu_{0} i}{4 R}$
$=\frac{\mu_{0} i}{2 R}$

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