question_answer

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

A) \[{{\mu }_{0}}\frac{i}{4R}\]                                         

B) \[{{\mu }_{0}}\frac{5i}{4R}\]

C)  \[{{\mu }_{0}}\frac{3i}{4R}\]                                     

D) \[{{\mu }_{0}}\frac{i}{2R}\]

Correct Answer: C

Solution :

                 \[{{B}_{1}}=\frac{{{\mu }_{0}}\times 2i}{2\times R}\] Similarly,    \[{{B}_{2}}=\frac{{{\mu }_{0}}i}{4R}\]                 \[{{B}_{net}}=\frac{{{\mu }_{0}}i}{R}-\frac{{{\mu }_{0}}i}{4R}=\frac{{{\mu }_{0}}i}{2R}\]