A) \[\frac{{{B}_{y}}}{{{B}_{X}}}=1\]
B) \[\frac{{{B}_{y}}}{{{B}_{X}}}=2\]
C) \[\frac{{{B}_{y}}}{{{B}_{X}}}=\frac{1}{2}\]
D) \[\frac{{{B}_{y}}}{{{B}_{X}}}=\frac{1}{4}\]
Correct Answer: C
Solution :
If R is the radius of coil X, men the radius of coil Y is 2R. The magnetic fields at O due to X and Y are respectively. \[{{B}_{X}}=\frac{{{\mu }_{0}}}{2}\frac{I{{R}^{2}}}{{{({{R}^{2}}+{{d}^{2}})}^{3/2}}}\] and \[{{B}_{Y}}=\frac{{{\mu }_{0}}}{2}\frac{I{{(2R)}^{2}}}{{{[(2{{R}^{2}}+{{(2d)}^{2}})]}^{3/2}}}\] \[\therefore \frac{{{B}_{Y}}}{{{B}_{X}}}=\frac{{{2}^{2}}}{{{({{2}^{2}})}^{3/2}}}=\frac{1}{2}\]You need to login to perform this action.
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