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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


E = BANωsinθ = BANωsin(ωt)

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

Maximum e.m.f (Eo) = 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 (Er.m.s) = BANω/21/2

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.

© Keith Gibbs 2020