A) \[1:\sqrt{2}\]
B) \[1:2\]
C) \[1:2\]
D) \[\sqrt{3}:1\]
Correct Answer: A
Solution :
Suppose the magnetic field produced due to each coil is B. The two coils are kept perpendicular hence, the angle between these is\[90{}^\circ \]therefore, the resultant magnetic field is given by \[=\sqrt{{{B}^{2}}+{{B}^{2}}+2B.B.\cos 90{}^\circ }\] \[=\sqrt{2{{B}^{2}}+2{{B}^{2}}\times 0}=\sqrt{2{{B}^{2}}}=B\sqrt{2}\] Hence, the ratio of magnetic field due to one coil and the resultant magnetic field is given by \[=\frac{B}{\sqrt{2}B}=1:\sqrt{2}\]
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