A) \[\frac{{{I}_{e}}R}{{{I}_{c}}\pi }\]
B) \[\frac{{{I}_{c}}R}{{{I}_{e}}\pi }\]
C) \[\frac{\pi {{I}_{c}}}{{{I}_{e}}R}\]
D) \[\frac{{{I}_{e}}\pi }{{{I}_{c}}R}\]
Correct Answer: A
Solution :
Magnetic field at the centre O of the loop of radius is \[{{B}_{1}}=\frac{{{\mu }_{0}}lc}{2R}\] Magnetic field due to the straight wire at the centre is \[{{B}_{2}}=\frac{{{\mu }_{0}}le}{2\pi H}\] For net field to be zero \[{{B}_{1}}={{B}_{2}}\,\,\,\Rightarrow \,\,\frac{{{\mu }_{o}}{{l}_{c}}}{2R}=\frac{{{\mu }_{o}}{{l}_{e}}}{2\pi H}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,H=\frac{{{l}_{e}}R}{\pi {{l}_{c}}}\]
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