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Question
Obtain the expression for the instantaneous value of emf induced.
Solution
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`
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