question_answer

Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre, find the ratio of the magnetic field due to one coil and the resultant magnetic field by both coils, if the same current is  flown [BHU 2003; CPMT 2004]

A)            1: \[\sqrt{2}\]                      

B)            1 : 2

C)            2 : 1                                          

D)            \[\sqrt{3}\,\,:\,\,1\]

Correct Answer: A

Solution :

           \[{{B}_{1}}={{B}_{2}}=B=\frac{{{\mu }_{0}}}{4\pi }\times \frac{2\pi i}{r}\] \[{{B}_{net}}=\sqrt{2}B\] \[\Rightarrow \frac{B}{{{B}_{net}}}=\frac{1}{\sqrt{2}}\]