A) \[\frac{{{\mu }_{0}}i}{2\pi r}\]
B) \[\left( \frac{{{\mu }_{0}}i}{4\pi r} \right)\,(\pi +2)\]
C) \[\left( \frac{{{\mu }_{0}}i}{4\pi r} \right)\,(\pi +1)\]
D) \[\left( \frac{{{\mu }_{0}}i}{4\pi r} \right)\,(\pi -2)\]
Correct Answer: B
Solution :
Magnetic field due to a straight wire of semi-infinite length is \[\frac{{{\mu }_{0}}i}{4\pi r}\] Magnetic field due to semicircular area is given by \[\frac{{{\mu }_{0}}i\,\pi }{4\pi r}\] \[\therefore \,\,\,\,\,\,\,\,\,\,B={{B}_{a}}+{{B}_{b}}+{{B}_{c}}\] \[=\,\,\,\,\,\,\,\frac{{{\mu }_{0}}}{4\pi }\frac{i}{r}+\frac{{{\mu }_{0}}i}{4\pi r}+\frac{{{\mu }_{0}}}{4\pi }\frac{i}{r}=\left( \frac{{{\mu }_{0}}i}{4\pi r} \right)(\pi +2)\]You need to login to perform this action.
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