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Two coplanar and concentric coils 1 and 2 have respectively the number of turns N_(1) and N_(2) and radii r_(1) and r_(2) (r_(2) gtgt r_(1)). Deduce the expression for mutual inductance of this system. |
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Answer» SOLUTION :Let us have two concentric coils of no. of turns `N_(1)` and `N_(2)` and radii `r_(1)` and `r_(2) (r_(2) gtgt r_(1))`. Let a CURRENT `I_(2)` flows through the OUTER coil no 2. Then magnetic field at the COMMON centre of coils. `B=(mu_(0)N_(2)I_(2))/(2r_(2))` Since `r_(1)ltltr_(2)` field may be considered to be uniform across entire coil no 1. Hence, total magnetic flux linked with inner coil is : `phi_(1)=N_(1)BA_(1)=N_(1)B(pi_(1)^(2))=N_(1)xx(mu_(0)N_(2)I_(2))/(2r_(2))xxpir_(1)^(2)=(mu_(0)piN_(1)N_(2)r_(1)^(2)l_(2))/(2r_(2))`  `therefore` Mutual inductance of the system M =`(phi)/(I_(2))=(mu_(0)piN_(1)N_(2)r_(1)^(2))/(2r_(2))` |
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