A) \[\frac{{{\mu }_{0}}i}{4\pi r}\]
B) \[\frac{{{\mu }_{0}}i}{4\pi r}+\frac{{{\mu }_{0}}i}{2\pi r}\]
C) \[\frac{{{\mu }_{0}}i}{4r}+\frac{{{\mu }_{0}}i}{4\pi r}\]
D) \[\frac{{{\mu }_{0}}i}{4r}-\frac{{{\mu }_{0}}i}{4\pi r}\]
Correct Answer: C
Solution :
B at 0 will be due to the following portions (i) vertical straight portion. This is zero. (ii) circular portion. This is given by \[{{B}_{circular}}=\frac{1}{2}\frac{{{\mu }_{0}}i}{2r}=\frac{{{\mu }_{0}}i}{4r}\] (iii) straight horizontal portion. This is given by \[{{B}_{straight}}=\frac{{{\mu }_{0}}i}{4\pi i}\] \[\therefore \]\[{{B}_{Total}}=\frac{{{\mu }_{0}}i}{4r}+\frac{{{\mu }_{0}}i}{4\pi r}\]
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