A) \[\frac{{{I}_{e}}R}{{{I}_{c}}\pi }\]
B) \[\frac{{{I}_{e}}R}{{{I}_{e}}\pi }\]
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 R is given by \[{{B}_{1}}=\frac{{{\mu }_{0}}{{I}_{c}}}{2R}\] where \[{{I}_{c}}\] is the current flowing in the loop. Magnetic field due to straight current carrying wire at a distance H, i.e., at the point O is given by \[{{B}_{2}}=\frac{{{\mu }_{0}}{{I}_{e}}}{2\pi H}\] For magnetic field to be zero at the centre of the loop, \[{{B}_{1}}={{B}_{2}}\] That is, \[\frac{{{\mu }_{0}}{{I}_{c}}}{2R}\,\,=\,\,\frac{{{\mu }_{0}}{{I}_{e}}}{2\pi H}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,H=\frac{{{I}_{e}}R}{\pi {{I}_{c}}}\]
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