Suppose a coil of area `5m^(2)`, resistance `10Omega` and number of turns 200 held perpendicular to a uniform magnetic field of strengh `0.4`T. The coil is now turned through `180^(@)` in time 1 s. What is
(i) average induced emf
(ii) average induced current
(iii) total charge that flows through a given cross-setion of the coil?

Explanation

Given, area of coil, `S=5m^(2)`, resistance, `R=10Omega`, number of turns, N = 200, magnetic field, B = `0.4T,Deltat=1s`.
When the plane of coil is perpendicular to the magnetic field i.e.,`theta_(i)=0^(@)`. And after it is rotated through `180^(@)`, then
`theta_(f)=180^(@)`.
`rArr"Initial flux,"phi_(i)=NBS cos 0^(@)=NBS`
`=200xx0.4xxs=400Wb`
and final flux =NBS `cos 180^(@)=-NBS=-400Wb`
`rArr"Change in flux",|Deltaphi_(B)|`
`=NBS-(-NBS)=2NBS=800Wb`
(i) Average induced emf `(epsilon)=(|Deltaphi|)/(Deltat)=(2NBA)/(Deltat)=800V`
(ii) Average induced emf `=(epsilon)/(R)=(2NBA)/(Deltat)=80A`
(iii) Average change `=(DeltaQ)/(Deltat)=(2NBA)/(RDeltat)`
`rArr" Total charge "DeltaQ=(2NBA)/(R)=80C`