The original question was: An electric field stores energy. Energy has mass if I understand E=mc2 correctly.
Now imagine a lone electron. It has an electric field. And therefore that field has mass presumably. If I apply a force to that electron, it will accelerate according to F=ma. My question relates to the m in F=ma.
The electric field must still exist even when the electron is moving. So therefore I am ALSO “moving” the electric field as well as the electron. So the m in F=ma must be made up of two parts, one of which is the mass component of the electric field and one of which just relates to the electron itself? Is that correct or am I confused. PS I appreciate it will be incredibly small and I also appreciate there may also be a magnetic field due to the changing electric field.
Physicist: You’re exactly right. The electric field has mass (or, at the very least you could say that it has inertia and attracts things gravitationally), because it carries energy. The energy density, K, of the electric field around a charge, q, is 
You can think of the energy in the field like a mess of Jello™ that’s thick near zero then thins out in all directions. If you push the charge in the middle, the Jello™ will also move, but the movement will take the form of a jiggly wave that propagates outward. That wave is where all the extra energy goes.
Electromagnetic energy.
Dropping the metaphor; pushing on a charge generates an electromagnetic (EM) wave. So applying a force to something with a charge (like electrons) takes more energy than it should (based on the mass alone), because the act of pushing on it generates a spray of photons (which is light, which is EM waves).
WOW!!!! so cool!!! Thanks for sharing your knowledge!!!
An electric field that can balance an electron of mass 3.2×10power-27 kg is———–
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Actually there is a big misunderstanding in the physicist’s answer which seems to be very common for some reason even among experts. He says that the electric field has mass because it has energy stored in it. This is simply not true. Not all forms of energy have an equivalent mass. For example, the photon has no rest mass but carries energy, E. Just by using Einstein’s formula and saying that m=E/c^2 is a kind of mass that we can attribute to the photon actually brings about a confusion over the role of the concept called mass in physics. Because although this formula is true, it means nothing in this case. What’s more, this kind of mass is not even unique because it is transformed if we change the frame of reference. And since it is transformed in the same way as energy, it is basically the same as the energy and coining another name for it does not lead to another physical quantity.
We must understand that mass is not a prime concept in relativity, only another form of energy (which is called rest energy) and just a part of the total energy of a particle or macroscopic object. While in nonrelativistic physics mass, energy and momentum are all conserved during the physical processes, it turns out that in relativistic physics mass is not conserved at all. It composes only a part of the total energy of an object that must be taken into account when we want to keep track of the total energy balance. Only energy and momentum are conserved so these two remain to be prime concepts but mass does not.
So, based on this, what can we say about the mass-energy equivalence? That it is true as long as we can give a meaning to mass independently of this formula as well, so that the formula creates equivalence between two quantities existing in their own right. For example, we can measure the mass of an electron independently of its electric field so deriving its mass from its electric field does make sense. But saying that the electromagnetic field in general has mass because it has energy makes no sense at all. EM field has energy, linear momentum and angular momentum because these are all conserved quantities and so prime concepts. But mass is something which does not necessarily have any meaning in a situation. So I would say that we have to be cautious with using it too frequently.
As for the other statement (that EM filed attracts things gravitationally), it is true. But not because it is its mass that attracts things gravitationally but because the source of gravity is not mass alone but the energy-momentum tensor. This has 16 components of which only one is the mass. The rest are energy and momentum density currents and the stress tensor.
Unfortunately (or not unfortunately) electromagnetism is intrinsically relativistic, so its deeper understanding can not lack the understanding of special or even general relativity as well.
The similarity between Newton’s second law and Einstein’s mass-energy equation cannot be denied. F=ma and E =mc^2 which show that both force and energy are equal to the product of mass and acceleration, albeit when the acceleration term is c^2
That this is true is demonstrated in the confined electrostatic fields of a fully charged capacitor. That field is measured in Newton’s per coulomb, i.e force and charge which provide a means of efficient storage of energy, the normal application of capacitors.
The point made here is that contrary to the notion that it does not make sense to associate electric fields with mass, rearranging Newton’s F=ma shows not just E/c^2 = mass, but also F/c^2 =mass. Thus the potentially phenomenal forces that can exist in the electrostatic field between the surfaces of a capacitor, do indeed equate to inertial mass. Capacitors are a large scale demonstration of the binding energy between protons and electrons, and the mass that is associated with the forces of attraction inside atoms, electric forces estimated to apply down to 10^-13 cm according to an analysis by Richard Feynman, Vol 1. ch 12 Feynman lectures on Physics.
The question of whether a capacitor has more mass/inertia when it is charged than when it is discharged (due to the potential electric energy or electric field translating into additional mass) could have huge consequences.
For instance, if a capacitor is made part of an electrical oscillator, causing it to charge and discharge at regular intervals (let’s say 10,000 cycles per second), and that capacitor is also mounted on a mechanical oscillator (a vibrating arm or piezzo stack) that causes it to physically move back and forth at the same frequency, so that the capacitor will always be at maximum charge on the up-swing, and at minimum charge at the down swing, then the up-swing would carry more momentum than the downswing, causing a net acceleration in the up-swing direction.
The electrical oscillating circuit would probably need to handle huge currents, preferably using a superconducting coil, and energy would definitely need to be fed into the system (no perpetual motion here), but we would effectively have propellant-less acceleration, just like the em-drive and mach-drive claim.
Hoping to find someone with a better understanding of the underlying physics to explain to me why this theoretical system would or would not work…
Thanks!
Even half a century after the death of Professor Richard Feynman, his three volume series of lectures on physics, and his book on the theory of quantum electrodynamics, (QED as it is better known), His books may be justifiably considered among the most authoritative and accessible on the subject, since he was awarded a third share of the 1965 Nobel Prize for physics for his contribution to that theory, which incidentally is one of the most tested in the history of physics, and no significant difference exists between theory and experiment.
As far as future propulsion is concerned, only virtual-massless electric fields and associated forces mediated by photons, have the potential to circumvent the ejection of mass in order to achieve a net change of momentum. The ‘law’ of equal and opposite reactions, conceived over three centuries before the advent of special relativity and quantum mechanics, is incompatible with relativistic fields that propagate at the speed of light, and therefore contrary to Newton’s third law which implies instantaneous action and reaction. NASA tested asymmetric capacitors during the Breakthrough Propulsion Physics programme between 1996 and 2002, and discounted that approach. More promising, is the advent of laser technologies that provide quasi-uniploar ultrashort pulses with peak electric fields of MV/cm, when applied at ~THz repetition rates in large arrays, may well provide that elusive breakthrough in the not too distant future.
This may be overly simplistic, but that is how I like my physics. We are happy tp write electrical potential (volt) as kQ/r, and we are equally happy to write electrical potential energy as kqQ/r; I do not think that anyone would argue with the convertibility or potential to kinetic energy. Okay. One definition of “energy” is the ability to do work (and the work-kinetic energy theorem seems to hold.) Since kinetic energy is difference between total energy and rest energy (with its mass equivalent), one propose reasoning along the following chain: electrical potential => electrical potential energy=>electirc field=>force=>momentum=>kinetic energy=> mass equivalency. This does not precisely prove that an an electric field has inertial mass, but it lays out an heuristic approach with which to frame the question
There is one topology associated with electromagnetic energy that encompasses many major natural constants, included are the free space permittivity epsilon-nought, permeability, mu-nought. speed of light ‘c’ , Planks ‘h’ and finally Gravitation ‘G’.
The first published record of this topology is found in the 1884 paper “ On the Transfer of Energy in the Electromagnetic Field.” where J.H.Poynting wrote: 7: “The velocity of plane waves of polarised light on the electromagnetic theory may be deduced from the consideration of the flow of energy. If the waves pass on unchanged in form with uniform velocity the energy in any part of the system due to the disturbance also passes on unchanged in amount with the same velocity. If this velocity be v, then the energy contained in unit volume of cubical form with one face in a wave front will all pass out through that face in 1/vth of a second.”
A cube of spacetime emerges as a natural but abstract topology, that may be defined by dimensions in terms of the wavelength cubed of a volume that bounds a quantised amount of radiation in accord with the Planck equation E=hc/wavelength or E=hf, and also from the natural orthogonal relationship between the electric and magnetic vectors to the Poynting energy flow vector
. where one corner of the cubic volume is perceived to be the origin of the three vectors, and the overall dimensions by the wavelength of a single quantised amount of energy.The origin of the Planck relationship itself is implied at the lowest energy boundary where the frequency is a single Hertz and wavelength is 300 million km, and the energy density according to both Poynting and Planck is implied equivalent to the Planck’s h!
At the opposite end of the energy spectrum, the high energy limit of the cubic volume, the wavelength is that of the Planck length, ~1.6E-35 meters, alongside the gravitational constant in the Planck length equation. The fundamental energy-frequency relationship as stated implies the same amount of energy in every cubic volume between and including 3E8 meters cubed and 1.6E-35 meters cubed, and suggests that this cubic volume of spacetime may serve as the long awaited link between Gravity and quantised energy.
I therefore commend this to the forum for further discussion.
“For example, the photon has no rest mass but carries energy, E. Just by using Einstein’s formula and saying that m=E/c^2 is a kind of mass that we can attribute to the photon actually brings about a confusion over the role of the concept called mass in physics. Because although this formula is true, it means nothing in this case. ”
The above is so wrong! The photon has relativistic mass which is why its reception transfers momentum. E = mc^2 equates for storage. Kinetic mass (rest mass) stores potential, intrinsic energy; kinetic energy (the photon) stores potential (relativistic) mass.