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Prove theoretically the relation between e.m.f. induced in a coil and rate of change of magnetic flux in electromagnetic induction.

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#### 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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