Consider a coil of N turns and area A being rotated at a constant angular velocity θ in a magnetic field of flux density B, its axis being perpendicular to the field (Figure 1). When the normal to the coil is at an angle θ to the field the flux through the coil is BAN cosθ = BAN cos(ω)t, since θ = ωt.

Therefore the e.m.f E generated between the ends of the coil is:

E = -d(φ)/dt = -d(BANcosθ)/dt

Therefore:

The maximum value of the e.m.f (E

At this point the wires of the coil are cutting through the flux at right angles – they chop through the field lines rather than slide along them.

Coil positions and output voltage

Example problem Calculate the maximum value of the e.m.f generated in a coil with 200 turns and of area 10 cm

E= BANω = 0.1x10

Notice the use of radians per second.