I How are Lenz's law and Faraday's law connected?

Lenz's law and Faraday's law are basically same. In case of electromagnetic induction the 'direction' of induced emf is crucial. Induced emf is given by the equation ## V = - \frac {d\phi}{dt}##. ##V## is induced emf and ##\phi## is magnetic flux. The minus sign is important because it protects the energy conservation principle. Faraday was completely aware of the result including the direction of the sign of emf. But it was Lenz who first introduced the minus sign into the emf-magnetic flux equation.

 

best to think of them as the laws of electromagnetic induction. One gives the size of the effect, the other gives the direction of the effect.