From what I know, wherever there is an electric field that is propagating, there will be a magnetic field present too, because that's what an EM wave comprises of- if it is going to carry energy, we will have both of them at any instant. But in any problem or application, there is this notion of applying the "Electric field" or "Magnetic field", what exactly does that mean? How are we ignoring the effects of the other? I do not get how that would work, because even for a stationary charge, the field is propagating but only consider it to have an electric field- but then what about the magnetic field?
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2 Answers
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I'm not sure to understand your question. I'll give it a try.
In some cases, when considering a plane wave incident on a molecule for instance, you only need to consider the electric force because: $$\frac{f_{e}}{f_{m}} = \frac{E}{vB} = \frac{c}{v}$$
and $c\gg v$. Therefore, sometimes, it depends on the settings of the problem and what effect you are studying. It would be helpful if you share a specific example.
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$\begingroup$ It is just a general question, like for example when we say that we are applying a magnetic field to a block of metal, what exactly does that mean? like I tried to make sense of just electric fields using what you have mentioned before as well, that the relative magnitude of electric fields is much greater than that of magnetic fields, so we ignore that term, but how can then one explain the notion of applying 'just magnetic fields'? $\endgroup$ Commented Jan 29, 2023 at 9:36
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$\begingroup$ Let's say you're looking at the reflection of an EM wave on a perfect conductor. If you want the surface current density that appears at the surface, you just have to compute the magnetic field before and after the surface. You would need only the magnetic field component of the wave to do just that. $\endgroup$– sazanCommented Jan 29, 2023 at 10:55
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$\begingroup$ But the electric field would be affecting the current density too, how can we explain that? $\endgroup$ Commented Jan 31, 2023 at 13:26
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How to make an electric field without a magnetic field:
We take electrons, put them in a box, where they move around. Outside of the box there is the sum electric field of the electric field of each electron, and the sum magnetic field of magnetic field of each electron. The sum of the small electric fields is non-zero, while the sum of the small magnetic fields is zero.
How to make a magnetic field without an electric field:
We take electrons, force all of them to move the same way, which creates a macroscopic magnetic field, and also creates a macroscopic electric field.
Then we add protons that we do not force to move the same way, which creates a macroscopic electric field that cancels out the macroscopic electric field that was created by the electrons, but does not create any macroscopic magnetic field.
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$\begingroup$ I understand that, but my question is that like you said there would be a net electric field outside the box, so it is propagating right, which is why it is found outside the box and if the wave is propagating, then it means there is a corresponding magnetic field, what about that? $\endgroup$ Commented Jan 31, 2023 at 13:25
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$\begingroup$ @Meganmars I don't know what you mean by the electric field that propagates. Electric field of electron is a ball shaped thing, and the center of the ball is where the electron is. If the center of the ball stays at the same position, then the field does not move, and there is no magnetic field. $\endgroup$– stuffuCommented Feb 1, 2023 at 22:21