The magnitude of the emf induced in the coil of the A.C generator is given by:

Explanation

The equation for the magnitude of the emf induced in the coil of an AC generator is:ε = NBAωsinθWhere:ε (varepsilon): Represents the induced emf (electromotive force) in volts (V).N: Represents the number of turns in the coil.B: Represents the magnetic field strength (in Tesla).A: Represents the area of the coil (in square meters).ω (omega): Represents the angular velocity of the coil (in radians per second). This is related to the rotational frequency (f) by the equation ω = 2πf.θ (theta): Represents the angle between the normal vector of the coil and the magnetic field direction (in degrees or radians).This equation represents a specific case of Faraday's Law of electromagnetic induction, applied to a rotating coil in a uniform magnetic field. Here's what each term signifies:NBA: This product represents the magnetic flux (Φ) passing through the coil. As the coil rotates, the area of the coil exposed to the magnetic field and the angle between them change, leading to a change in the magnetic flux.ωsinθ: This term represents the rate of change of the magnetic flux with respect to time (dΦ/dt). The sine function accounts for the fact that the rate of change is maximum when the coil is perpendicular to the field (θ = 90°) and zero when the coil is parallel to the field (θ = 0° or 180°).Therefore, the equation accurately depicts the magnitude of the induced emf in the AC generator, considering the number of turns, magnetic field strength, coil area, angular velocity, and the orientation of the coil relative to the field.