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Two concentric circular coils, one of small radius r_(1) and the other of large radius r_(2), such that r_(1)ltltr_(2), are placed co-axially with centres coinciding. Obtain the mutual inductance of the arrangement. |
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Answer» SOLUTION :Let a CURRENT `I_(2)` flow through the OUTER circular coil. The field at the centre of the coil is `B_(2)=(mu_(0)I_(2))/(2r_(2))`. Since `r_(1)ltltr_(2),B_(2)` may be considered constant over cross-sectional area of the other coil. Hence, flux linking with it is `phi_(1)=pir_(1)^(2)B_(2)=(mu_(0)pir_(1)^(2))/(2r_(2))I_(2)=M_(12)I_(2)` Thus, `M_(12)=(mu_(0)pir_(1)^(2))/(2r_(2))` from equation (3) and (6) `M_(12)=M_(21)=(mu_(0)pir_(1)^(2))/(2r_(2))` |
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