E.m.f. generated in a rotating coil

           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:

E = BANωsinθ = BANωsin(ωt)

The maximum value of the e.m.f (E_o) is when θ (= ωt) = 90^o (that is, the coil is in the plane of the field, Figure 2) and is given by

Maximum e.m.f (E_o) = BANω

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.

The r.m.s value of the e.m.f is (E_r.m.s) = BANω/2^1/2

Coil positions and output voltage

Example problem
Example problem Calculate the maximum value of the e.m.f generated in a coil with 200 turns and of area 10 cm² rotating at 60 radians per second in a field of flux density 0.1 T.

E= BANω = 0.1x10^-3 x 200 x 60 = 1.2 V

Notice the use of radians per second.