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Two conducting loops of radii R_1 and R_2 are concentric and lie in the same plane. If R_1 bb R_2 , the mutual inductance M between them will be directly proportional to
- R_1 R_2
- R_2/R_1
- R_2^2/R_1
- R_2^2 R_1
Correct answer: R_2^2/R_1
Solution
When R_1 bb R_2 , the magnetic field due to the larger loop is nearly uniform over the smaller loop. The field at the center of a circular loop is proportional to 1/R_1 , and the flux through the smaller loop is proportional to its area ( R_2^2 ) . Hence M propto R_2^2/R_1 .
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