A) zero
B) \[\frac{{{\mu }_{0}}I}{4\pi a}\]
C) \[\frac{{{\mu }_{0}}I}{2\pi a}\]
D) \[\frac{{{\mu }_{0}}I}{2\sqrt{2}\pi a}\]
Correct Answer: C
Solution :
Sections AB and \[D\varepsilon \] produce no field at O. Sections BC and EF produce equa fields at O magnetic field at O \[{{B}_{1}}=\frac{{{\mu }_{0}}I}{4\pi a}\,\,\left[ \cos \,o-cos\frac{\pi }{2} \right]\] [Because wire is long] \[\Rightarrow \] \[{{B}_{1}}=\frac{{{\mu }_{0}}I}{4\pi a}\] (in magnitude) Similar \[{{B}_{2}}=\frac{{{\mu }_{0}}I}{4\pi a}\] (in magnitude) \[\therefore \] Net field at 0, \[B={{B}_{1}}+{{B}_{2}}\] \[\Rightarrow \] \[B=\frac{{{\mu }_{0}}I}{2\pi a}\]
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