A) \[\frac{{{\mu }_{0}}i}{2\pi r}\]
B) \[\left( \frac{{{\mu }_{0}}}{4\pi } \right)\left( \frac{i}{r} \right)(\pi +2)\]
C) \[\left( \frac{{{\mu }_{0}}}{4\pi } \right)\left( \frac{i}{r} \right)(\pi +1)\]
D) \[\frac{{{\mu }_{0}}i}{4\pi r}(\pi +1)\]
Correct Answer: B
Solution :
Field due to a straight wire of infinite length is \[\frac{{{\mu }_{0}}i}{4\pi r}\]if the point is on a line perpendicular to its length while at the centre of a semicircular oil is\[\frac{{{\mu }_{0}}\pi i}{4\pi r}\]. \[\therefore \] \[B={{B}_{a}}+{{B}_{b}}+{{B}_{c}}\] \[=\frac{{{\mu }_{0}}}{4\pi }\frac{i}{r}+\frac{{{\mu }_{0}}}{4\pi }\frac{\pi i}{r}+\frac{{{\mu }_{0}}}{4\pi }\frac{i}{r}\] \[=\frac{{{\mu }_{0}}}{4\pi }\frac{i}{r}(\pi +2)\]out of pageYou need to login to perform this action.
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