A) \[\frac{{{\mu }_{0}}I}{2\pi R}\]
B) \[\frac{{{\mu }_{0}}nI}{2R}\]
C) \[\frac{{{\mu }_{0}}nI}{2\pi R}\left( \pi +1 \right)\]
D) \[\frac{{{\mu }_{0}}nI}{2\pi R}\left( \pi -1 \right)\]
Correct Answer: C
Solution :
Magnetic field due to long wire at 0 point \[{{B}_{1}}=\frac{{{\mu }_{0}}}{2\pi }\left( \frac{I}{R} \right)\] (upward direction) Magnetic field due to loop at O point \[{{B}_{2}}=\frac{{{\mu }_{0}}}{4\pi }.\frac{I.2\pi R}{{{R}^{2}}}\] \[{{B}_{2}}=\frac{{{\mu }_{0}}}{2}.\frac{I}{R}\](in upward direction) Hence, resultant magnetic field at centre O \[B={{B}_{1}}+{{B}_{2}}\] \[B=\frac{{{\mu }_{0}}I}{2\pi .R}(\pi +1)T\]You need to login to perform this action.
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