A large circular loop of radius b b has a current I b Ib passing through it. The loop is held horizontally with its plane parallel to the ground. A much smaller circular loop of radius a a ( a << b a<

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The formula for mutual inductance of two concentric loops

Explanation:

Generally magnetic field in a concentric coplanar loop  is mathematically represented as

         Where is the permeability o free space

                     R is the radius

                    is the current

The magnetic flux  of two concentric loops is mathematically represented as

      a is the area

Generally magnetic inductance is mathematically represented as

Substituting for   in the above equation

i'm only doing this for the points : (

explanation:

i'm only doing this the points

no. dot product   =0 when vecs at right angles