A) infinite
B) zero
C) \[\frac{{{\mu }_{0}}2i}{4\pi R}\pi \]
D) \[\frac{{{\mu }_{0}}2i}{4\pi R}(\pi +1)\]
Correct Answer: D
Solution :
The magnitude of magnetic field at 0 due to the straight part of wire is \[{{B}_{1}}=\frac{{{\mu }_{0}}}{2\pi }\frac{i}{r}\] \[{{B}_{1}}\]is perpendicular to the plane of page, directed downwards. The field at the centre O due to current loop of radius r is \[{{B}_{2}}=\frac{{{\mu }_{0}}i}{2r}\] ...(ii) \[{{B}_{2}}\]is also perpendicular to page, directed upwards. \[\therefore \]Resultant field at O is \[{{B}_{1}}+{{B}_{2}}=\frac{{{\mu }_{0}}i}{2r}\left( \frac{1}{\pi }+1 \right)\] \[=\frac{{{\mu }_{0}}2i}{4\pi r}(\pi +1)\] Perpendicular to page directed upwards.You need to login to perform this action.
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