What type of current is induced in a dc generator when magnets are rotated?

The simple explanation as to why a change in the coil causes a change to the electric current is that the electric field and the magnetic field are the same field and they exist in a four dimensional quaternion space.

Change in a quaternion space is four dimensional and when you take the derivative there is a real derivative d/dr=d/cdt and a vector derivative Del

X= d/dr + Del = d/cdt + Id/dx + Jd/dy + Kd/dz.

The answer to this question is the Quaternion four space derivative of the vector Electric Field, Ev.

(d/dr + Del)Ev= -Del.Ev + dEv/dr + DelxEv = -Del.Ev + dBv/dt + DelxEv

The Quaternion Derivative is X=d/dr + Del = d/cdt + Del

The vector part of the derivative dB/dt + DelxEv is the answer to the question this can be transformed by introducing the coil with dA as the area and dC as the circumference:

dBv/dt.dA + DelxEv.dA = AdB/dt + Integral loop Ev.dC