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Elsewhere on Stack Exchange several people have said that the average, mean or RMS value of the magnetic field of an AC-electromagnet would be about the same, or slightly lower than, a DC one. But, the peak value of the AC field would be higher than the DC one. (Assuming same voltage, etc.) Why?

How could a changing current, in and of itself, produce, even very momentarily, a higher/stronger magnetic field?

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  • $\begingroup$ The answer to this question really depends on what you mean by "assuming same voltage". Typically there are two ways of deciding what "the voltage" of an AC supply is. If by "the voltage" you mean "the peak voltage", then an AC supply will never exceed a DC supply at "the same voltage". If, instead, you use the more common definition, which sets "the voltage" to be "the root-mean-square voltage", then, since the peak voltage of AC current is higher than the root-mean-square voltage, the peak voltage of an AC supply will exceed the voltage of a DC supply set at the rms voltage. $\endgroup$ – probably_someone Jun 14 at 15:37
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enter image description here

An AC-electromagnet will oscillate, probably through something quite similar to a sine wave. A DC magnet has a constant strength. Often the effective strength of an AC magnet can be approximated by its root-mean-square strength, the square root of the average of the square of its instantaneous strength. For a sine wave this is $\frac{1}{\sqrt{2}}$ times the amplitude. This is shown in the graph. As you can see, for a portion of the curve the sine wave is above it's RMS value.

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  • $\begingroup$ Good answer, puppetsock. Thanks for the visual aid. But it still blows my mind that changing the direction of the current can somehow, even very briefly, create a field (any field) that is stronger than if you just let the current run in one direction.... $\endgroup$ – Kurt Hikes Jun 14 at 14:33
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    $\begingroup$ "For a sine wave this is $\sqrt{2}$ times the amplitude" - Typo? $\endgroup$ – Hal Hollis Jun 14 at 15:28
  • $\begingroup$ @HalHollis Yes. Fixed. $\endgroup$ – puppetsock Jun 14 at 15:30
  • $\begingroup$ @KurtHikes, I can make an AC signal with 1 microamp rms current or 100 amp rms current. Or with 1 uA DC current or 100 A DC current. The 1 uA AC current has much smaller peak current than the 100 A DC current. The 1 uA AC current only has a larger peak current than the 1 uA DC current because of how we choose to express the magnitude of the AC signal. If I had a 1 uA peak-peak AC current (i.e. $i(t)=0.5\ {\rm \mu A}\sin(\omega t)$), then it would have a lower peak current than the 1 uA DC current. $\endgroup$ – The Photon Jun 14 at 15:49
  • $\begingroup$ @KurtHikes, or put another way, we use rms because a 1 A rms AC current (into a given resistive load) will deliver the same average power as a 1 A DC current. But since the AC current spends some time near 0, it must have peaks at higher than 1 A to deliver the same power on average. $\endgroup$ – The Photon Jun 14 at 15:51

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