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Two concentric circular coils, one of small radius r and the other of large radius R, such that R >> T, are placed coaxially with centres coinciding. Obtain the mutual inductance of the arrangement. |
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Answer» SOLUTION :Let a current `I_(2)` flows through the outer circular COIL of radius R. The magnetic field at the centre of the coil is `B_(2) = (mu_(0)I_(2))/(2R)` As r << R, hence field `B_(2)` may be considered to be constant over the entire cross-sectional area of INNER coil of radius r. Hence, magnetic flux linked with the smaller coil will be `phi_(1) = B_(2)A_(1) = (mu_(0) I_(2))/(2R).pur^(2)` As by definition `phi_(1) (2) = M_(12)I_(2)` `therefore` Mutual INDUCTANCE `M_(12) = (phi_(1))/I_(2)=(mu_(0)pir^(2))/R.` But `M_(12) = M_(21) = M` `therefore` Mutual inductance of pair of concentric coils`M = (mu_(0) pir^(2))/R`. 
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