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Electric Charges And Fields

Question
CBSEENPH12040094
Wired Faculty App

Two coils of self-inductances 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is

  • 10 mH

  • 6 mH

  • 4 mH

  • 16 mH

Solution

C.

4 mH

When the total flux associated with one coil links with the other i.e, a case of maximum flux linkage, then
        straight M subscript 12 space equals space fraction numerator straight N subscript 2 straight ϕ subscript straight B subscript 2 end subscript over denominator straight i subscript 1 end fraction space space space and space space space straight M subscript 21 space equals space fraction numerator straight N subscript 1 straight ϕ subscript straight B subscript 1 end subscript over denominator straight i subscript 2 end fraction
Similarly,    straight L subscript 1 space equals space fraction numerator straight N subscript 1 straight ϕ subscript straight B subscript 1 end subscript over denominator straight i subscript 1 end fraction space space space space and space space straight L subscript 2 space equals space fraction numerator straight N subscript 2 straight ϕ subscript straight B subscript 2 end subscript over denominator straight i subscript 2 end fraction
If all the flux of coil 2 links coil 1 and vice-versa then
                       straight ϕ subscript straight B subscript 2 end subscript space equals space straight ϕ subscript straight B subscript 1 end subscript
Since,     straight M subscript 12 space equals space straight M subscript 21 space equals space straight M comma hence we have
          straight M subscript 12 straight M subscript 21 space equals space straight M squared space equals space fraction numerator straight N subscript 1 straight N subscript 2 straight ϕ subscript straight B subscript 1 end subscript straight ϕ subscript straight B subscript 2 end subscript over denominator straight i subscript 1 straight i subscript 2 end fraction space equals space straight L subscript 1 straight L subscript 2
therefore space space space space space space space straight M subscript max space equals space square root of straight L subscript 1 straight L subscript 2 end root Given comma space space space space space space space space space straight L subscript 1 space equals space 2 mH comma space space space space straight L subscript 2 space equals space 8 space mH therefore space space space space space space space space straight M subscript max space equals space square root of 2 cross times 8 end root space equals space square root of 16 space equals space 4 space mH

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point? 

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