In my revision guide it says that Michael Faraday did experiments that showed that induced e.m.f for a coil of wire depends on four things:
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Magnetic strength of the core in the coil of wire. (stronger –> bigger emf)
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Number of turns of wire in the coil (more turns –> bigger emf)
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The cross-sectional area of the coil (bigger area –> bigger emf). (This could also be seen as the angle you point the magnet at the coil, because flux linkage is basically the same as flux cutting.)
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How fast you move the magnet into/out of the coil. (Faster –> bigger emf)
But Faraday's law seems to not show all four of these:
$\text{induced emf}=N\frac{\Delta \phi}{\Delta t}$.
(Sorry I don't know calculus yet which is why I didn't use the calculus version)
This equation shows that induced emf only depends on two things:
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Number of turns of wire $N$.
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How fast you move the magnet.
Where did the others go? :
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Area of the coil.
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Magnetic strength of the core.
Best Answer
$\text{induced emf}=N\frac{\Delta \phi}{\Delta t}$.
where,$\phi $ is the magnetic flux through the coil.
The flux, $\phi $ depends on both the area of the coil, the magnetic field through the coil and the angle between the direction of magnetic field and the area vector of the coil ( area vector is perpendicular to the plane of the coil ). And the equation of magnetic flux goes as $\phi $ = BAcos$ \theta $. The flux through a coil is changed by changing any one of these parameters.So, the flux has a direct relation to the area of the coil.
A core can increase the magnetic field to many times the strength of the actual field through the coil alone, due to the "magnetic permeability $ \mu $ " of the material where $ \mu $ depends on the "Magnetic strength of the core material". Hence, B depends on the magnetic strength of the core material also.Hence, the magnetic flux too.