Electromagnetic Induction

Mutual conductance depends on the relative position and orientation of the two coils.

The induced $emf$ is

$e = {{ - d\phi } \over {dt}} = - {{d\left( {\overrightarrow B .\overrightarrow A } \right)} \over {dt}}$

$ = {{ - d\left( {BA\cos {0^ \circ }} \right)} \over {dt}}$



$\therefore$ $e = - B{{dA} \over {dt}} = - B{{d\left( {\ell \times x} \right)} \over {dt}}$

$ = - B\ell {{dx} \over {dt}} = - B\ell v$

These three inductors are connected in parallel. The equivalent inductance ${L_P}$ is given by

${1 \over {{L_P}}} = {1 \over {{L_1}}} + {1 \over {{L_2}}} + {1 \over {{L_3}}}$ $ = {1 \over 3} + {1 \over 3} + {1 \over 3} = {3 \over 3} = 1$