A) \[\frac{{{\mu }_{0}}i}{4}\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right)\]
B) \[\frac{{{\mu }_{0}}i}{4}\left( \frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}} \right)\]
C) \[\frac{{{\mu }_{0}}i}{4}({{R}_{1}}-{{R}_{2}})\]
D) \[\frac{{{\mu }_{0}}i}{4}({{R}_{1}}+{{R}_{2}})\]
Correct Answer: A
Solution :
In the following figure, magnetic fields at O due to sections 1, 2, 3 and 4 are considered as \[{{B}_{1}},\,{{B}_{2}},\,{{B}_{3}}\] and \[{{B}_{4}}\] respectively. \[{{B}_{1}}={{B}_{3}}=0\] \[{{B}_{2}}=\frac{{{\mu }_{0}}}{4\pi }.\frac{\pi \,i}{{{R}_{1}}}\otimes \] \[{{B}_{4}}=\frac{{{\mu }_{0}}}{4\pi }.\frac{\pi \,i}{{{R}_{2}}}\]¤ As \[|{{B}_{2}}|\,\,>\,\,|{{B}_{4}}|\] So \[{{B}_{net}}={{B}_{2}}-{{B}_{4}}\Rightarrow {{B}_{net}}=\frac{{{\mu }_{0}}i}{4}\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right)\otimes \]You need to login to perform this action.
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