A) \[\frac{{{\mu }_{0}}}{4\pi }\frac{i}{r}tesla\]
B) \[\frac{{{\mu }_{0}}}{4\pi }\frac{i}{r}tesla\]
C) \[\frac{{{\mu }_{0}}}{4\pi }\frac{i}{2r}tesla\]
D) zero
Correct Answer: B
Solution :
From Biot-Savarts law, the magnetic field at a point distant r from a current element\[\delta l\]is \[\delta B=\frac{{{\mu }_{0}}}{4\pi }\frac{i\delta l\sin \theta }{{{r}^{2}}}\] where\[\theta \]is the angle between the element\[\delta l\]and the line joining the element to that point. For each straight part of wire\[\theta =0\](or\[{{180}^{o}}\]). Hence, for each straight point, we have \[{{B}_{1}}={{B}_{2}}=0\] The field at centre 0 due to the semi-circular current loop of radius r is \[{{B}_{3}}=\frac{1}{2}\left( \frac{{{\mu }_{0}}i}{2r} \right)=\frac{{{\mu }_{0}}i}{4r}\] Therefore, the field due to the full wire is \[{{B}_{3}}={{B}_{1}}+{{B}_{2}}+{{B}_{3}}=\frac{{{\mu }_{0}}i}{4r}\]teslaYou need to login to perform this action.
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