Question

Obtain the expression for the instantaneous value of emf induced.

Answer 1

Consider a coil of M turns and area A being rotated at a constant angular velocity ω in a magnetic field of flux density B, its axis being perpendicular to the field.

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.

Figure 1:

Figure 2:

`E = -(dphi)/(dt)`

`E = -(d(BAN costheta))/(dt)`

E = BAN ωsin(ωt)

The maximum value of the e.m.f. (E₀) is when θ = ωt = 90° (that is, the coil in the plane of the field as shown in figure) and is given by

`E_0 = BANomega`