# Electromagnetic factors affecting inertial mass of a body affect its gravitational mass or not?

We can see that when a charge sphere is at rest & we are to put it in motion with any desired velocity than we will have to apply the same force for a longer time as if it were applied to the identical uncharged sphere to put it in motion with the same desired velocity.Here the due to electromagnetic fields associated with the charged sphere are responsible for this fact & by methods of integration we find that the additional inertial property gained by the body due to its charge can be given by a simple function of universal constants charge of the body and its radii.I have varified that in linear as well as planar or 3d motion we can apply normal mechanics by adding this factor of additional inertial property in its actual mass.so in one way we can say that the particle show more inertia without any external interference to it so its inertial mass is increased.And I have read that all experiments till today show that inertial mass and gravitational mass are completely identical.so due to charge on any body its gravitational mass is also changed affected or not ?

• Out of curiosity, what is your justification for your first sentence? Is it a lenz's law type argument? – Brian Moths Apr 27 '14 at 21:01
• bcoz if we assume any particle which is charged is to led to a desired velocity we have to perform more work on it as compared to that on an identical chargeless particle because with the moving charge a magnetic field is set up & its corrosponing magnetic field energy is to be supplied by us.Basically we perform work on the particle & even if it is differnert in the two cases considered the particle gaon same speed beause the changing magnetic field will induce the electric field & that will oppose the motion of the particle.Somewhere it may be thought as a consequence with lenz rule... – Dvij Mankad Apr 27 '14 at 21:07
• Could you please expand the question? What you are asking is extremely unclear. Are you saying that the electromagnetic self-force on a charged sphere alters the mechanics of the sphere in a way that looks like a mass? Please add the jist of a clear derivation and break your question up into paragraphs so it is readable and parseable. – Jerry Schirmer Apr 30 '14 at 22:44
• All shouting comments have been removed. – dmckee May 1 '14 at 16:38
• In response to a deleted comment from @Dvij that this question is based on electromagnetic mass according to the work of Bruce Harvey, Physics Stack Exchange has a policy of discussing mainstream physics. Bruce Harvey states that mainstream physics "out-weirds science fiction", as stated on his site: bearsoft.co.uk/original_index.html – DavePhD 4 hours ago – DavePhD May 1 '14 at 20:29

When you try to accelerate a charged body, Abraham–Lorentz force will also act on it, effectively reducing the acceleration. This doesn't imply larger mass. The momentum transferred to the body has been taken away by the electromagnetic field, not by some "extra mass" of the charged body. If you accelerate a charged body you will produce electromagnetic radiation and electromagnetic radiation carries away the momentum.

However, regarding more general case, if you do have an effect that increases inertial mass of a body, that effect should also, by equivalence principle, increase its gravitational mass.

Feynman does exactly this calculation (momentum/energy of a moving charged sphere) in his Lectures on Physics (volume 2, chapter 28), and indeed there is a term due to the charge which behaves exactly like mass (i.e. $\frac{dp}{dv} = m + k q^2$ for $v \ll c$ where $q$ is the charge on the sphere and $k$ is some constant). This is distinct from the Abraham-Lorentz force mentioned in the other answers (which is proportional to the rate-of-change of acceleration and therefore is not equivalent to an additional mass). As Danijel points out, the equivalence principle implies that the change in inertial mass of a charged sphere must also affect its gravitational mass.

• can you suggest website or etc from where this lectures are available..thanx in adv... – Dvij Mankad May 12 '14 at 16:35
• @Dvij The Feynman Lectures on Physics are freely available at feynmanlectures.caltech.edu – Danijel May 12 '14 at 20:30

That is an interesting question. My point of view is the following one. When you accelerate abruptly a charged body, some energy is released in the environment via photons and you must pay energy for that, on top of the kinetic energy you want to give to the body. In other words, the system is not closed: you must consider that when you exert a force on the charged body, some other bodies (photons) will appear and will carry away energy, momentum and also mass.

The inertial mass of the body I believe that is not changed because of the following fact: if you accelerate slowly (say adiabatically) the body, then no magnetic field nor photons will be created. So you won't lose energy and the body will respond to the adiabatic force as any other uncharged body. That being so, it means that inertial mass of charged and uncharged bodies are the same (at least under an adiabatic force).

Now, coming back to before and analyze more deeply. If you consider an abrupt change of motion (non adiabatic force) and this will create some electromagnetic field around the moving body (bremsstrahlung), then some photons will be created which are responsible for that. Such photons will carry away energy, momentum and also mass. Then, the mass of the whole system of photons plus accelerated body is the inertial and gravitational mass of the system, which is surely bigger than in the previous adiabatic case. However, the mass pertaining to the charged accelerated body should be the same. In other words, the system "is not closed", which is to say that when you accelerate the charged body you will have to consider additional particles that are going away from it. If you don't do that, then you will soon find that energy is not conserved, which is very troublesome. At the end of the day, Pauli postulated the neutrinos exactly for this reason: some energy must have been taken away by something in beta decay, unless we were to accept that energy was not conserved.

Work done on an object is given by the change in potential energy of the object. When an object moves from lower potential to a higher potential then work done is negative and vice versa.

If a charged mass is set in motion under neutral conditions(no free charges and external magnetic field present in the vicinity) the work done in moving the given mass is equal to the work done in moving similar uncharged mass. The work done in creating magnetic field is zero because magnetic field produced is in the perpendicular direction of motion of charged body.

The above case is valid under neutral conditions. When charges and magnetic field are present the work done maybe positive or negative depending on potential difference.

Mass is always constant when no external factors interfere. Charge cannot change mass of ann object. Then why do electrons and protons have same charge but different masses? Mass changes only when the frame of reference changes i.e., theory of general relativity.

The charge and mass are completely independent of each other.

Difference between inertial mass and gravitational mass is given in detail in the following url:

What's the difference between the five masses: inertial mass, gravitational mass, rest mass, invariant mass and relativistic mass?