A) \[{{\mu }_{0}}i(\pi -1)/2\pi r\]
B) \[{{\mu }_{0}}i(\pi +1)/2\pi r\]
C) \[{{\mu }_{0}}/2\pi r\]
D) none of the above
Correct Answer: A
Solution :
According to the question, the magnetic field due to straight part of the conductor at the centre is given by \[=\frac{{{\mu }_{0}}i}{2\pi r}\] Now the magnetic field due to a circular part of wire at the centre \[=\frac{{{\mu }_{0}}i}{2r}\] These two fields are in opposite direction Therefore, net field \[=\frac{{{\mu }_{0}}i}{2r}-\frac{{{\mu }_{0}}i}{2\pi r}=\frac{{{\mu }_{0}}i}{2\pi r}(\pi -1)\]
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