Faraday's law of EMI:

$$ E\text{(induced emf)}=-\frac{d\Phi}{dt}\tag{1}$$

Here: $\Phi$= magnetic flux across the surface enclosed by the loop.


Q1- Is the $\Phi$(magnetic flux) in (1) the total flux (net $\Phi$)

A situation to clarify Q1
A bar magnet's $N$-pole is brought closer to a "CircularLoop(CL)" of wire at a constant velocity. So, $\Phi$ across the CL increases. An emf is produced in CL which produces a magnetic field opposing the bar magnet's N-pole. Now their will be some $\Phi$(flux) due to this opposing magnetic field and will decrease the (net $\Phi$ ) across the CL.

So two things:

  1. Bar magnet comes closer, $\Phi$ increases across CL
  2. Induced emf creates Opposing Magnetic Field(OMF), and $\Phi$ due to OMF results in decrease of $\Phi$ across the CL

So, in (1) above, do we take net flux (net $\Phi$)? So, Faraday's law is that if there is change in net flux ($\Phi$ net) then emf is induced?

Q2- If your answer to Q1 is "yes we take net flux", then why do i see that in so many derivations, the $\Phi$ due to OMF is ignored and Faraday's law is applied by considering just the change in $\Phi$ due to External Magnetic Field?
For eg, this derivation for motional emf: Derivation of formyla for motional emf....pdf link:https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.aapt.org/docdirectory/meetingpresentations/SM15/Mungan2015.pdf&ved=2ahUKEwjyiqXyvvHyAhWESH0KHXanAZ8QFnoECCYQAQ&usg=AOvVaw1n8zQuDVjyKqh4SM4iRTIl


  1. I searched across the web but nowhere was this aspect explicitly mentioned. See wikipedia:https://en.m.wikipedia.org/wiki/Faraday%27s_law_of_induction
  2. I have tried my best to make this post readable by making abbreviations along with their full forms in the text itself.
  3. Link of "motional emf eg." pdf:https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.aapt.org/docdirectory/meetingpresentations/SM15/Mungan2015.pdf&ved=2ahUKEwj1-9qXyvHyAhVKXSsKHU8cD98QFnoECD8QAQ&usg=AOvVaw1n8zQuDVjyKqh4SM4iRTIl

1 Answer 1


It is, as I think you have decided, the net flux that is responsible for the net induced emf. However, we can write the net emf as $$\mathscr E = -\frac{d\Phi}{dt}=-\frac{d(\Phi_{ext}+\Phi_{ind})}{dt} = -\frac{d\Phi_{ext}}{dt}+\left(-\frac{d\Phi_{ind}}{dt} \right)= \mathscr E_{ext}+\mathscr E_{ind}$$ Here, $\Phi_{ext}$ is the flux from outside the circuit and $\mathscr E_{ext}$ the emf that can be attributed to the rate of change of that flux. $\Phi_{ind}$ is the flux arising from the induced current at some instant and $\mathscr E_{ind}$ is the emf that can be attributed to the rate of change of that flux.

In many textbook treatments, $\mathscr E_{ind}$ is not at first mentioned. It is often dealt with later under the heading of self induction, an effect that comes into play only when the circuit is complete.

This two-stage treatment of the induced emf may be worrying for the alert student!

  • $\begingroup$ Hi! thanks for the excellent answer.So, all the results (like eg. of motional emf i gave in Question) derived without considering Self induction are wrong? $\endgroup$ Commented Sep 9, 2021 at 11:17
  • $\begingroup$ (a) Thank you. (b) Wrong? That's a bit strong. The 'partitioning' of flux and emf in the manner I have outlined is so widespread, that I doubt if many would object to calling $Blv$ the motional emf even with $B$ as the external flux density. $\endgroup$ Commented Sep 9, 2021 at 11:40
  • $\begingroup$ \\1)So, i should just consider not including effect of (self induction) a simplification and move on?\\2) Sorry but I couldn't get what are you trying to say---"The 'partitioning' of flux and emf in the manner I have outlined is so widespread, that I doubt if many would object to calling Blv the motional emf even with B as the external flux density." $\endgroup$ Commented Sep 9, 2021 at 14:15
  • $\begingroup$ (1) Yes, but be aware of the 'self-flux' aspect when the circuit is complete. In elementary work you probably won't be given enough information to compute the flux due to the induced current, so you won't be able to take quantitative account of its effects in any case! (2) Could you please say what bit didn't you understand? $\endgroup$ Commented Sep 9, 2021 at 15:03
  • $\begingroup$ 1)Flux due to OMF(see ques.) was not considered in deriving final result Blv. Then you thought "wrong" was a bit strong. So i did not understand what your thoughts on the result were. Did you consider "Blv" a fair result, or did you think most people would not consider "Blv" a correct result..(basically the sentence i quoted from your comment was not clear what it was trying to say...)\\2)Anyhow, your answer was very helpful. $\endgroup$ Commented Sep 9, 2021 at 15:46

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