Define ‘mutual inductance’ of to coil. On what factors it depends? Two concentric circular coils, one of small radius r1 and the other of large radius r2, such that r1 << r2, are placed co-axially with centres coinciding. Obtain the mutual inductance of the arrangement.


Mutual induction is the process of induction of voltage in one coil due to the change in current of another coil close to it.


It is measured by the mutual inductance of the coil, L, given by the relation: ɸ1 = Li2... (i) where ɸ1 = flux through first coil, i2 = current flowing through second coil.


Diagram of problem:



Let the two loops carry currents i1(r1) and i2(r2) respectively.


Magnetic field induced at the centre due to the bigger loop(B),



Where μ0 = magnetic permeability


Flux induced through the first coil = B x area of first coil,


= Li2, according to (i).


Therefore, L is given by



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