Question on Faraday's Law

  • Thread starter yungman
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  • #1
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Main Question or Discussion Point

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
 

Answers and Replies

  • #2
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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
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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
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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
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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
5,439
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I am only guessing about your reference.

You really need to supply more detail please.
 
  • #7
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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.
 

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