A) \[\frac{{{\mu }_{0}}\pi {{R}_{2}}}{R}\]
B) \[\frac{{{\mu }_{0}}{{R}_{2}}}{\pi {{R}_{1}}}\]
C) \[\sqrt{2}{{\mu }_{0}}\,\pi R_{1}^{2}R_{2}^{2}\]
D) \[\frac{{{\mu }_{0}}\pi R_{2}^{2}}{2{{R}_{1}}}\]
E) \[2\frac{{{R}_{1}}{{R}_{2}}}{{{\mu }_{0}}\,\pi }\]
Correct Answer: D
Solution :
Let the current through the outer loop is \[I\]. The magnetic field at the common centre O is \[B=\frac{{{\mu }_{0}}I}{2{{R}_{1}}}\] As,\[{{R}_{2}}<<{{R}_{1}},\]the flux of magnetic field through it will be approximately \[\phi =\frac{{{\mu }_{0}}I}{2{{R}_{1}}}\pi R_{2}^{2}\] Now, mutual inductance, \[M=\frac{\phi }{I}=\frac{{{\mu }_{0}}\pi R_{2}^{2}}{2{{R}_{1}}}\]You need to login to perform this action.
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