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Reverse of faraday's law

  1. Oct 28, 2008 #1
    faraday's law states that if there is a change in the magnetic flux inside a conductor, a potential is induced across the ends. Is the opposite also valid, i.e. if I have a current carrying conductor with a constant potential applied across the ends, will there be a change in the magnetic flux inside the area of the current carrying conductor?

    If this is not true, why is it not true?
  2. jcsd
  3. Oct 28, 2008 #2
    The key word is change.
  4. Oct 29, 2008 #3
    Faraday's law is bi-directional. In your question you mentioned "current carrying conductor with a constant potential applied across the ends". Is the "constant potential" you refer to time changing? If it is, then yes, the magnetic flux inside the loop area will vary with time.

    Under time-varying conditions, E & B (or E & H) cannot exist independently of one another.
  5. Oct 29, 2008 #4
    let me rephrase my question:

    In mathematical terms fardays law states that

    Integral(E.dl) over a circuit = -k*d/dt(Integral(B.n.da))

    here dl is an infinitesimal length along the circuit, n is the normal to the area of the circuit and da is an infinitesimal cross-section within the circuit.

    I accept this to be true, but nowhere do I find any mention of the reverse of the law, i.e.

    -k*d/dt(Integral(B.n.da)) = Integral(E.dl) over a circuit

    in otherwords if I keep the Integral(E.dl) over a circuit constant or at some particular value by using a constant voltage source, Integral(B.n.da) is supposed to decrease with time. Is this true too?

    The reason I ask this is that Faraday's law is extrapolated to the differential form, and forms part of the maxwells equation. Now a differential equation is always bi-directional, but if the equation from which the differential equation is derived is not bi-directional, then the differential equation should be wrongly formulated.
  6. Oct 29, 2008 #5


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    I'm not very sure about the mathematical part, i.e. the directions of a differential equation.
    but what faraday's law says is: a changing magnetic flux causes electric potential, but it's not the only way to create an electric potential, which does not cause a changing magnetic (it rather causes a constant magnetic field around it.
    anyway, a changing electric potential, causes a changing magnetic field, which causes a changing electric potential, which causes a changing magnetic field...
  7. Oct 30, 2008 #6
    I'm astonished at the question. The order of the variables wrt to the equal sign is irrelevant. The theorem of Pythagoreus can be expressed as c^2 = a^2 + b^2, or as a^2 + b^2 = c^2, or a^2 = c^2 - b^2, etc.

    Also, the equations functionally relate the variables and do not infer pecking order or causality. Just as distance equals rate times time, time = distance/rate, rate = distance/time, etc.

    Anyway, a transformer is a perfect example of the bidirectional nature of Faraday's law. Let's use a voltage xfmr since they are much more common than current xfmrs. A constant voltage ac source is connected to the primary. A time changing magnetic flux/field will exist in the core. Thus a time-changing primary voltage and its accompanying time-changing magnetizing current give rise to a magnetic flux, also time-changing. This time-changing flux, in turn, gives rise to secondary current and voltage, both time-changing.

    Thus a given V forces a phi (flux), just as a given phi forces a V.

    A similar analogy holds for Ampere's law. The relation between phi and I is also bidirectional. I hope this helps. BR.

  8. Oct 30, 2008 #7
    Thanks claude for your answer. It did clear up my doubt. The difference between the mathematical analogy that you showed and my problem is that the equation that I wrote is just a mathematical representation of a physical phenomena. While the Pythagoras equation is a purely mathematical identity. Now if the physical phenomena itself is not bi-directional, the mathematical representation too wouldn't be so. The thing is most electrodynamics books start deriving the Faraday's equation using the analogy of a magnet and a circuit, but they dont mention the opposite effect, yet they go on to derive the differential equation.

    I have basically a background in thermal sciences, and intuitively I can say that all laws in my area are bidirectional, but I am not sure whether all physical laws are the same. Is there any exception to this rule of bi-drectionality?
  9. Oct 30, 2008 #8
    I cannot think of any exceptions to the bi-directional nature of physical laws, not to say that there aren't any. I just can't think of one.

  10. Oct 31, 2008 #9
    you are given a loop in space. if integral(E.dl) has some value on this loop, then how do you get this sort of field?a ststic charge or a system of static charges make it zero due to superposition principle. So u need a current out there so a magnetic field.
    I think, you just cant make line integral of electric field finite without a magnetic field.
  11. Nov 3, 2008 #10
    That's the nature of fields. Under time-variation, E & H fields cannot exist independently of one another. As Master Yoda would put it, "always two there are, never goes one without the other." Thus a time changing E coexists with a time changing H. The induced fields consist of E & H mutually. Which one comes first is an endless vicious circle.

    Also, you are correct that a system of static charges would result in zero potential around a closed loop. The E field due to static charges is conservative, i.e. around a closed path gives zero. The E field due to induction is non-conservative, i.e. around a closed path is non-zero since said E field has "curl" or "rotation".

    Does this help? BR.

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