# Induced e.m.f depends on…?

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:

1. Magnetic strength of the core in the coil of wire. (stronger --> bigger emf)

2. Number of turns of wire in the coil (more turns --> bigger emf)

3. 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.)

4. 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:

1. Number of turns of wire $N$.

2. How fast you move the magnet.

Where did the others go? :

1. Area of the coil.

2. Magnetic strength of the core.

• The quantities you are missing determine the actual value of the flux $\phi$, so the hard stuff, like the influence of the magnetic core material and the actual shape of the field, has been tucked away in this version. – CuriousOne May 8 '15 at 13:31
• @CuriousOne: Great, thanks! I think this would make a good answer (instead of comment) if you expand it. – user45220 May 8 '15 at 14:37

$\text{induced emf}=N\frac{\Delta \phi}{\Delta t}$.
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.
• $\vec{B}$ is the magnetic field and $\vec{A}$ is the area of the loop. – Apoorv Potnis May 1 '17 at 12:19