A) \[\frac{\sqrt{5}{{\mu }_{0}}I}{2R}\]
B) \[\frac{3{{\mu }_{0}}I}{2R}\]
C) \[\frac{{{\mu }_{0}}I}{2R}\]
D) \[\frac{{{\mu }_{0}}I}{R}\]
Correct Answer: A
Solution :
The magnetic field (B) at the centre of circular current carrying coil of radius R and current \[I,B=\frac{{{\mu }_{0}}I}{2R}\]Similarly, if current \[=2I\], then Magnetic field \[=\frac{{{\mu }_{0}}2I}{2R}=2B\] So, resultant magnetic field \[=\sqrt{{{B}^{2}}+{{(2B)}^{2}}}=\sqrt{5{{B}^{2}}}=\sqrt{5}B\] \[=\frac{{{\mu }_{0}}I\sqrt{5}}{2R}\]
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