The inductors of two LR circuits are placed next to each other, as...

${ε}_{1} = {L}_{1}\dfrac{d{i}_{1}}{dt} + M\dfrac{d{i}_{2}}{dt}$

$d{W}_{1} = {ε}_{1}{i}_{1}dt$

$= {L}_{1}\left(d{i}_{1}\right){i}_{1} + M\left(d{i}_{2}\right){i}_{1}$

$d{W}_{2} = {L}_{2}\left(d{i}_{2}\right){i}_{2} + M\left(d{i}_{1}\right){i}_{2}$

$d{W}_{1} + d{W}_{2} = {L}_{1}{i}_{1}\left(d{i}_{1}\right) + {L}_{2}{i}_{2}\left(d{i}_{2}\right) + Md\left({i}_{1} \cdot {i}_{2}\right)$

$W = \dfrac{1}{2}{L}_{1}{i}_{1}^{2} + \dfrac{1}{2}{L}_{2}{i}_{2}^{2} + {M}_{1}{i}_{2}$

$= 55mJ$,

Note : If mutual induction is taken in opposite direction then $W = 35mJ$