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I was reviewing a homework problem I completed for class, but I saw different explanation that contradict each other.

My teacher says that this position for the waves is optimal for maximum induced current since it is perpendicular to the changing magnetic field as the field is moving right, having all of the induced voltage is from the magnetic field only.

But the book solutions say that since the loop is not moving through the magnetic field, it is unable to induce a current in the conductor. Since the loop is at rest, the magnetic field will not induce any current. So, it is up to the electric field to induce the voltage such that being parallel to the electric field will induce the current.

Which is right? Are both of them correct depending on the wave? Is there a situation where a combination of the two would produce the maximum current? Is this really the best way to place the waves?


1 Answer 1


To get a feel for what is going on think of the magnetic field that a stationary current in a circular loop generates. Here is a picture from 2:


As you can see the maximum of the magnetic field is along the symmetry axis of the loop. Now if your loop is used as a receiver antenna then from reciprocity considerations the largest field coupling should occur also when the magnetic field is parallel with the symmetry axis and this is what your drawing implies. (Probably it would be better to say that the maximum current or the maximum emf is induced and not the potential but that is a side issue.)

You may wish to think of the dual problem that is consider a linear dipole radiator and explain why the electric field should be parallel with the dipole for maximum coupling.

The above considerations assume that the loop perimeter is much shorter than the wavelength and thus the current is essentially uniform. Consequently the distribution of the loop's magnetic field is similar to that of the stationary case. On the contrary, if the perimeter is longer than the wavelength this is not the case and coupling from/with the E-field is also possible.

  • $\begingroup$ Asking for explanative purposes. So it depends on how big the loop is? Also, is the current or induced emf only coming from the electric field in this question, but for bigger loops, it comes from the magnetic field since it varies? $\endgroup$
    – xosonah682
    Commented May 11, 2021 at 1:09
  • $\begingroup$ Faraday's law: A time varying magnetic field induces an electric field. An axial magnetic field will induce a circumferential electric field, hence the current in the loop. An electric field that is parallel with the metal can induce an oscillating current that in turn can radiate but it is the same effect as that of the magnetic field and the latter is easier to analyze for a loop. If the E field is perpendicular to the loop then it cannot generate any current (infinitesimal thin cross section) just as the H field is incapable of coupling to the loop. $\endgroup$
    – hyportnex
    Commented May 11, 2021 at 1:30
  • $\begingroup$ If the loop is "long" (> wavelength) then the radiation pattern along with the current is more complicated but even then it would be difficult to couple the E field that is perpendicular to a very thin wire. Given that the wire is thin but not infinitely thin there must be some amount of coupling even if E is has no parallel component with the wire and the longer the circumference the easier the loop will radiate/absorb. At any rate this E-field coupling to a perpendicular wire is likely to be (I am guessing now) a second order effect. $\endgroup$
    – hyportnex
    Commented May 11, 2021 at 1:37
  • $\begingroup$ I did not consider Faraday's Law! That makes more sense, so essentially both are one in the same when considering the induced current is from the wave and we can use either magnetic/electric field to model the effect. Is that valid? I am a first year E&M student so I do not understand the coupling you are referring to. $\endgroup$
    – xosonah682
    Commented May 11, 2021 at 2:03
  • $\begingroup$ It is more conventional to use the word "induce" than "couple". I used "couple" here because I wanted to avoid the unidirectional implication of the word "induce" in the sense that the "time varying field E (or H) CAUSES the other field H (or E)". In reality, one field does not the make the other field for they are always made together by time varying currents and time varying charges. "Coupling" is the proxy for "being induced together", I hope this wording helps for I suspected from your otherwise completely fine question that you are just starting to learn about this. $\endgroup$
    – hyportnex
    Commented May 11, 2021 at 12:38

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