α : the initial position of the coil,
S : the area formed by the coil, and
θ : the angle between the magnetic fi eld and the area formed by the coil.
Therefore, the EMF induced in the coil is
e = ΩNBSsin(Ωt +α).
Figure 4.34: Induced EMF in a coil.
When given coil, placed in a fi xed magnetic fi eld, rotates at a constant
speed, EMF is induced in the coil. The induced EMF varies sinusoidally in the
time domain (Figure 4.35), and its amplitude is proportional to the rotational
speed of the coil.
From Figure 4.34 and equations 4.54 to 4.56, the peak values of the back-
EMF appear at the positions where the coil axis is vertical to the magnet axis,
and the zero crossing positions of the back-EMF happen at the locations where
the coil axis is along with or opposite to the magnet axis. These are similar to
the Ampere's torque discussed in section 4.2.3.
Using the commutation system shown in Figure 4.20, the alternating EMF
can be recti fi ed to one shown in Figure 4.36. It contains DC component as
well as harmonics.