Question

There is a small square wire frame of side length inside a large square wire frame of side length L (l < concentric and coplanar with it. If side length of large square frame is doubled, then the mutual inductance between them

Answer 1

Given :

Length of the side of small square = l

Length of the side of large square = 2L

To Find :

The mutual inductance between the squares

Solution :

• The relation between mutual inductance and lengths of the squares is

                 $M \propto \frac{l^{2} }{L^{2} }$

• Initially the length of larger square is L

                $M \propto \frac{l^{2} }{L^{2} }\rightarrow Equation (1)$

• The length of the larger scale is doubled i.e., 2L

               $M_{1} \propto \frac{l^{2} }{(2L)^{2} }$

               $M_{1} \propto \frac{l^{2} }{4L^{2} }\rightarrow Equation(2)$

• By dividing equation (1) and (2) we get,

               $\frac{M}{M_{1}} = 4$

              $M_{1} = \frac{M}{4}$

   The mutual inductance between the squares becomes M/4