A coil is placed in a magnetic field as shown below: B

A current is induced in the coil because $\overrightarrow{B}$  is:

The first and second laws weren't created together and have a gap of many years between them. Earlier, he just found out a way to calculate whether the EMF was produced or not. But with time, its direction and magnitude also needed to be calculated which resulted in him giving a second law to support his belief.

Faraday's first law only tells us if the EMF is induced or not. Unlike the second law, it doesn't have any connection with the EMF's magnitude or direction. Therefore, only the second law of faraday has a formula since it is used to calculate both the magnitude and direction of the induced EMF.

The actual role of these laws is that faraday's law tells us the magnitude of induced EMF and Lenz's law was a modification of faraday which also could tell the direction of induced EMF. These two laws are combined together to form the base of any concept related to electromagnetic induction.

$V=\frac{-d?}{dt}=-\left(15t^2+8t+2\right)$

at t = 2 sec, V = - (15 × 4 + 8 × 2 + 2)

 = 78 V

$I=\frac{V}{R}=\frac{78}{5}=15.6A$

E = -dφ/dt = - (20t + 20) mV.
At t=5s, E = - (100+20) = -120mV.
I = |E|/R = 120mV/2Ω = 60mA.