• # question_answer Two circular coils X and Y, having equal number of turns, carry equal currents in the same sense and subtend same solid angle at point O. If the smaller coil X is midway between O and Y, then if we represent the magnetic induction due to bigger coil Y at O as By and due to smaller coil X at O as ${{B}_{X}}$ then A)  $\frac{{{B}_{Y}}}{{{B}_{X}}}=1$               B)  $\frac{{{B}_{Y}}}{{{B}_{X}}}=2$C)  $\frac{{{B}_{Y}}}{{{B}_{X}}}=\frac{1}{2}$              D)  $\frac{{{B}_{Y}}}{{{B}_{X}}}=\frac{1}{4}$

Solution :

Magnetic induction at 0 due to coil Y is given by,${{B}_{Y}}=\frac{{{\mu }_{0}}}{4\pi }\times \frac{2\pi I{{(2r)}^{2}}}{{{\left[ {{(2r)}^{2}}{{d}^{2}} \right]}^{3/2}}}$                    ??(1) Similarly, the magnetic induction at 0 due to coil X is given by         ${{B}_{X}}=\frac{{{\mu }_{0}}}{4\pi }\times \frac{2\pi I{{r}^{2}}}{{{\left[ {{r}^{2}}+{{(d/2)}^{2}} \right]}^{3/2}}}$     ??(2) From eq.(1) & (2)     $\frac{{{B}_{Y}}}{{{B}_{X}}}=\frac{1}{2}$

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