Some questions about electromagnetic waves.

[Coolamebe]

- What exactly is the equilibrium of the waves that is shown on graphs? My understanding is that the oscillations are in the strengths of the field, and different sides of the equilibrium represent different directions of the fields. However, I feel as though this contradicts itself in some ways. So when both fields are at equilibrium (as the electric and magnetic field oscillate in phase) how would a new field be generated? I though the two different fields were generated by each other and the propagation of the wave depended on these fields inducing each other, which keeps it propagating. But when at equilibrium (which by my thoughts mean that they are practically non-exist for a moment in time) they cannot induce the opposite field, as they have no strength.
- Does quantum mechanics discount this view of an EM wave propagating via the propagation of electric and magnetic fields? I was just wondering this as from just the propagation of fields, I see no way for some of the quantum effects regarding photons to occur, such as a photon transforming (I don't know if that is the right word or not) into an electron and a positron.

 

[blue_leaf77]

According to Maxwell equations, the emergence of one of the fields is induced by the rate of change, not the absolute value, of the other field. In the case of EM wave although at some point in time and space, both fields may disappear but the rate of change at this instant is not zero.

 

[Coolamebe]

I'm still in year 11, and so haven't really advanced far enough in math to understand Maxwell's equations. I can see some things I know, but for instance I have no idea what the integral with a circle around it means (though I'd be more than willing for anyone to explain the meaning or link any introductory resources). Is their any intuitive explanation for why it is the rate of change of the fields? My guess would be it is because it is an accelerating charge with induces both fields, and so an accelerating electric/magnetic field has the same inductive effect. Is that right?

 

[blue_leaf77]

Other than the integral form, Maxwell equations can also be written in differential form. This last form may give you a more transparent look about the dependence on the rate of change of the field. In terms of math, a rate of change of a quantity is expressed as the derivative of that quantity. As you see in the differential form of Maxwell equation, the "curl" (a kind of derivative) of electric field, written as $\nabla \times \mathbf E$, is proportional to the rate of change of $\mathbf B$ with respect to time, $\partial \mathbf B/\partial t$. In generalized term, Maxwell equations connect the rate of changes of electric and magnetic fields.

 

[Coolamebe]

Yep, that makes sense. So just to confirm, is my guess at the end of my post correct? I think I understand the very basic math behind it, and can see how that would result in the three dimensional wave diagram that all the pictures show, so I'm basically content with where I am at now. Even so, I like to have an intuitive explanation behind most ideas I come across, so I'm just wondering whether I can use my guess as the explanation.

 

[blue_leaf77]

My guess would be it is because it is an accelerating charge with induces both fields, and so an accelerating electric/magnetic field has the same inductive effect. Is that right?

While it is true that an accelerating charged body will emit EM wave, it's not the sole mechanism by which EM radiation is formed. Photons can also be produced during electronic transition in atoms or molecules. In these situations, the system is most appropriately described using quantum mechanics where the concept of acceleration is often not well-presented. Moreover, it's not correct to consider the field to be accelerating. When someone says "the rate of change of some field", it means the rate at which the magnitude of this field changes.