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Question
Prove theoretically the relation between e.m.f. induced in a coil and rate of change of magnetic flux in electromagnetic induction.
Solution
1)
Magnetic flux Φ = NABcos ωt
N → No.s of turns
A → Area of a coil
B → Magnetic field {external}
ω → Angular speed of the coil
`:. max phi_0 = NAB, omegat -> 0`
`:.phi = phi_0 cos omegat`
induce EMF(e)
e = `-(dphi)/(dt) = + omegaNAB sin omegat`
`e_0 = omegaNAB, omegat -> 90`
`:. e = e_0 sin omegat`
So there is phase difference of `pi/2` with `phi` and e
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