For a coil,

$$e=N\frac {d\Phi}{dt}$$

Where $e\;$ is the instantaneous voltage driving the coil and $\Phi\;$ is the flux generated through the coil with N turns.

For a coil

$$\oint \vec B \cdot d\vec l =\mu N I \Rightarrow B=\mu N I \Rightarrow \Phi = BS=\mu N I S$$

In the book Handbook of Transformer Design & Application by Flanagan, page 1.7, it gives

$$e=N\frac{d\Phi}{dt}\times 10^{-8}$$

It said the multiplier factor depends on the system units. I have no idea how that $10^{-8}\;$ comes from. Please help.

Thanks

Alan

I have never seen Flanagan, is it an old book?

The conversion factors between the old cgs system and MKS are

Magnetic flux density : 1 volt-second/metre2 = 104 emu (gauss)

Magnetic flux : 1 volt-second (weber) = 10 8 emu (maxwell)

Inductance : 1 henry = 109 emu

EMF : 1 volt = 108 emu

Thanks for the reply. I still have question:

$$\Phi = BS=\mu N I S$$

It $\Phi\;$ is in H/m X N X coulomb/sec X m^2. $\frac{d\Phi}{dt}\;$ is in (H/m X N X coulomb/sec X m^2)/sec

In the old cgs system one line of induction was called a maxwell, and magnetic induction expressed in maxwells per sq cm.

One maxwell per sq cm was called a gauss.

In MKS

1 weber per sq m = 104 gauss.

since 1 meter squared = 104 cm2 it follows that

1 weber = 108 maxwells

In the old cgs system one line of induction was called a maxwell, and magnetic induction expressed in maxwells per sq cm.

One maxwell per sq cm was called a gauss.

In MKS

1 weber per sq m = 104 gauss.

since 1 meter squared = 104 cm2 it follows that

1 weber = 108 maxwells
Yes, I actually studied they since you replied. My question is how to make the two side to be equal units as I posted in #3

Thanks

You really need to supply more detail please.

You really need to supply more detail please.
I am referring to this

It Φ is in H/m X N X coulomb/sec X m^2. dΦdt is in (H/m X N X coulomb/sec X m^2)/sec

On the left side, μ is in H/m, I is in A/sec, area is m^2. Then it is per second.
On the right side, it is Web per second.

I am still missing something.