(a) State the principle of an ac generator and explain its working with the help of a labelled digram. Obtain the expression for the emf induced in a coil having N turns each of cross-section area.
A, rotating with a constant angular speed `omega` in a magnetic filed `omega`, directed prependicular to the axis of rotation.
(b) An aeroplane if flying horizontally for west to east with a velocity of 900 km/hours. Calcuate the potential difference developed between the ends of its wings having a span of 20n. The horizontal component of the Earth's magnetic field is `5 xx 10^(-4) T` and the angle of dip is `30^(@)`.

Explanation

(a) AC generator : Consider a coil PQRS free ot rotate in the form of magnetic field B. The axis of rotation of the coil is prependicular to theB.
`N_(O/)`= NBA `cos(theta)`
`N_(O/)` = NBA `cos (omegat)`
`(Nd_(O/))/(dt) = NBA (d)/(dt)cos omegat`
`(Nd_(O/))/(dt)= NBA omega sin omegat`
`- epsi = - NBA omega sin omegat{epsi=(-Nd_(O/))/(dt)}`
`espi = espi_(0) sin omegat" "espi_(0) = NBA omega`
(b) `V = 900 xx (1000)/(3600) = 250m//s`
l = 20m
When aeroplane going from west to east, its wing cross vertical component of the Earth magnetic field.
`B = 50 xx 10^(-4)` Tesla
`theta = 30^(@)`
`B sin theta = B`
`B _(bot) = 5 xx 10^(-4) xx sin 30^(@) = 2.5 xx 10^(-14)`
`epsi = BIV = 2.5 xx 10^(-4) xx 20 xx 250 = 50xx 25xx10^(-3) = 1.25 xx 10^(-2) = 1.25 Volt`.