$i _{1}:$ Current in primary coil

$M$ : Mutual inductance

$e _{2}=- M \frac{ di _{1}}{ dt }$

$M =-\frac{ e _{2}}{\frac{ di }{ dt }}$

${[ M ]=\frac{\left[ e _{2}\right]}{\left[\frac{ di _{1}}{ dt }\right]}=\frac{\left[\frac{ W }{ q }\right]}{\left[\frac{ di _{1} }{ dt }\right]}=\frac{\left[ ML ^{2} T ^{-2}\right]}{\left[ \frac {AT}{AT^{-1}}\right]}}$

$=\left[ ML ^{2} T ^{-2} A ^{-2}\right]$