Suppose initially the plane of coil is perpendicular to the magnetic field B. When coil rotates with angular speed ω, then after time t, the angle between magnetic field \(\vec{B}\) and normal to plane of coil is
θ = ωt
∴ At this instant magnetic flux linked with the coil φ = BA cos ωt
If coil constants, N-turns, then emf induced in the coil
= +NBA ω sin ωt .....(i)
∴For maximum value of emf ε,
sin ωt =1
∴ Maximum emf induced, εmax = NBA ω