Power produced by an induction coil?
You start with the induction law:
$$U_{ind} = - \int \vec{E} \ d \vec{s}  = - \frac{ \partial }{\partial t}  \int {\vec B}\ d \vec{A}$$
This law says, that every change of the magnetic field in the cross section area of the closen wire winding leads to a certain induction voltage. The power is given by $$ P = \frac{U^2}{R} $$ where \$R\$ is the resistance of your consumer.
Regarding to Lenz' law, the induced current works &quot;against its cause&quot;. Therefore a higher resistance of the load increases the electrical power but takes more kinetic energy from the generator. The quanitative relation is given by inductivity $$ L = \frac{N^2}{R_M} $$ where \$N\$ is the number of windings and \$R_M\$ is the magnetic resistance of your magnetic circuit, which can be determined with some geometry. Then you need the time-dependency of the magnetic field through the coil. To aim a description of the process, you will not outflanks maths. But for your motivation you will find some easy experiments.