Understanding Faraday's Law for Coils: Exploring the Mysterious 10^-8 Multiplier

In summary: Please help.In summary, Flanagan says that the multiplier factor depends on the system units. I have no idea how that 10^{-8}\; comes from.
  • #1
yungman
5,708
240
For a coil,

[tex]e=N\frac {d\Phi}{dt}[/tex]

Where [itex]e\;[/itex] is the instantaneous voltage driving the coil and [itex] \Phi\;[/itex] is the flux generated through the coil with N turns.

For a coil

[tex]\oint \vec B \cdot d\vec l =\mu N I \Rightarrow B=\mu N I \Rightarrow \Phi = BS=\mu N I S[/tex]

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

[tex]e=N\frac{d\Phi}{dt}\times 10^{-8}[/tex]

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

Thanks

Alan
 
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  • #2
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
 
  • #3
Thanks for the reply. I still have question:

[tex]\Phi = BS=\mu N I S[/tex]

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

How does this become maxwell/sec in the equation? I am confused with the units. Please help.
 
  • #4
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
 
  • #5
Studiot said:
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
 
  • #6
I am only guessing about your reference.

You really need to supply more detail please.
 
  • #7
Studiot said:
I am only guessing about your reference.

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.
 

1. What is Faraday's Law?

Faraday's Law, also known as the law of electromagnetic induction, states that a changing magnetic field can induce an electric current in a conductor.

2. Who discovered Faraday's Law?

Faraday's Law was discovered by the English scientist Michael Faraday in the 1830s.

3. How is Faraday's Law used in everyday life?

Faraday's Law has many practical applications in everyday life, such as generating electricity in power plants, charging batteries, and powering electronic devices.

4. What is the mathematical equation for Faraday's Law?

The mathematical equation for Faraday's Law is E = -NΔΦ/Δt, where E is the induced electromotive force, N is the number of turns in a coil, and ΔΦ/Δt is the rate of change of magnetic flux.

5. How does Faraday's Law relate to Lenz's Law?

Faraday's Law and Lenz's Law are closely related, as Lenz's Law is a consequence of Faraday's Law. Lenz's Law states that the direction of the induced current will be in such a way as to oppose the change that caused it, as described by Faraday's Law.

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