# Do we need waves for fields?

I was pondering about EM Waves and fields and felt that there is an inconsistency in the physical picture of EM waves that I have in my mind. For example let us consider a charge at rest . Now lets say we want to test the electric field due to this charge Q at a point P. So to do this we need to place another charge at that point and find if we can feel any force due to that charge. Now I think for Q to exert a force on test charge or an electric field to be established at that point there must be EM waves propagating from the charge Q to the test charge. However there are no accelerating charges which are the prerequisites for EM waves to be generated . So this brings in an inconsistency in the physical picture of EM waves I have in my mind. I believe that there is some misconception I am having and I am positively looking forward to replies to clear it out.

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In classical physics, particles can communicate with each other through their fields which are assumed to have been set up long before we start to think about the problem, i.e. they do not need to have "EM waves propagating from the charge Q to the test charge". I think this is the source of your confusion. –  Chris Mueller Apr 1 at 15:30
@ChrisMueller Yes probably that's it ..how can we assume that something called field is inherent ? –  Primeczar Apr 1 at 15:35
To be honest, fields are a more fundamental concept in physics than particles. Your question would be better stated; how can particles (point like objects) arise out of fields (continuous objects which permeate all space)? Although I can give a hand-waving answer to that question, you are better off getting a reply from the theorists by asking a new question on phys.SE. –  Chris Mueller Apr 1 at 15:42
If you think of EM waves as analogous to ocean waves, think of electrostatic forces as analogous to ocean currents. –  Harry Johnston Apr 2 at 8:57

Now I think for Q to exert a force on test charge or an electric field to be established at that point there must be EM waves propagating from the charge Q to the test charge.

A wave would imply a forces that changes in time, but the force does not do that.

You could argue that you are talking about very long periods, but the DC limit is electrostatics.

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There is no need for a wave for a force to be exerted. The formula for the Lorentz force is $\mathbf{F} = q\mathbf{E} + q\mathbf{v}\times \mathbf{B}$. What this says is that even for a static electric field, such as that produced by a charge at rest, the test charge will feel a force $\mathbf{F} = q\mathbf{E}$, even if the field is not changing with time.

i would say your misconception lies in the statement "Now I think for Q to exert a force on test charge or an electric field to be established at that point there must be EM waves propagating from the charge Q to the test charge". Electromagnetism simply does not work like that. Waves will certainly cause a test charge to move, but they are not the only way. In fact, since waves are a combination of oscillating electric and magnetic fields, they will cause the test charge to move in a rather complicated way. A charge $Q$ at rest, however, produces a field $\mathbf{E} = \frac1{4\pi \epsilon_0}\frac{Q}{r^2}\hat{\mathbf{r}}$, and a test charge placed in such a field will move in a straight line, a quite different motion to that produced by a wave.

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Now let us consider the case of electric potential .At a given point electric potential is the amount of work done in bringing a charge from infinity to that point without any change in its kinetic energy .Now this means to bring the charge the agent needs to equal amount of work as done by the source charge. For the source charge to do work we definitely need EM waves if this is the only possible way to transmit energy ... –  Primeczar Apr 1 at 15:11
@Primeczar: I don't know why you say the source charge must do work. It's the one carrying the test charge from infinity who does the work. If the source charge did work equal to that, then there would be no change in energy for the test charge. –  Javier Badia Apr 1 at 15:22
@Primeczar The point here is that EM waves are not the only way to transmit energy. Static Electric fields exert forces on charged particles. –  George G Apr 1 at 15:24
@JavierBadia Thats what I was saying the agent as well as the source charge do equal amount of work resulting in no chnage in kinetic energy of the test charge . –  Primeczar Apr 2 at 11:56
@GeorgeG Thats what I was trying to know whether EM waves are the only way to transmit energy ..However is it so that the notion of fields is an assumed one...I mean is it so that it is assumed that a field exists for every charged particle through which it can influence other charged ones..something that is inherent to it..? Doesn't it seem awkward in assuming so? –  Primeczar Apr 2 at 11:59

your confusion is easy to resolve. think of Maxwell's equations. now look at them again but assuming that there is no time dependence, so all time derivatives will equal to zero. you'll get Gauss's Law this way. it's for static charges. you put a charge, it'll put a force on another charge as you described. no waves involved.

the waves are periodic solutions of the same Maxwell equations, they appear when there's time varying component, such as moving charges

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I haven't considered abt Maxwell's equation here because you can see I am doubting the physical foundations ... –  Primeczar Apr 1 at 15:17
ok, just think that there's a differential equation. it may have periodic or non-periodic (decaying) solution depending on the conditions. e.g. a guitar's string is described by differential equation. if you don't touch it, it's still. if you pluck it, it'll get back - but now there's some time-varying condition, which will bring the periodic solution, i.e. sound waves –  Aksakal Apr 1 at 15:25