Does charging my phone increase its gravitational force?

[Ebi]

TL;DR

Is this statement correct: "when I charge my mobile phone, according to E=mc^2, its mass increases, consequently, its gravitational force increases".

If the statement above is correct, I do not understand this concept. I guess by charging my phone I am not producing matter. Does it mean in this case, energy converts to mass (not matter)? Can someone please explain this?

 

[Ibix]

$E=mc^2$ is rather too simplistic for this, but basically yes. All forms of energy, not just mass, are sources of gravity in general relativity. Storing chemical potential energy in the battery does therefore increase its mass and its gravitational field, at least according to theory. The effect is indetectably small.

 

[Orodruin]

Mass is rest energy. It does not require something to be produced as ”matter”. The additional mass of your charged battery is mainly due to the increase in its internal energy.

In addition, ”energy” is not a thing that converts into other things. It is a property of different systems that is conserved when accounting for all contributions. What $E=mc^2$ really tells you is how the inertia of a system in its reat frame relates to its rest energy.

 

[pervect]

Summary:: Is this statement correct: "when I charge my mobile phone, according to E=mc^2, its mass increases, consequently, its gravitational force increases".

If the statement above is correct, I do not understand this concept. I guess by charging my phone I am not producing matter. Does it mean in this case, energy converts to mass (not matter)? Can someone please explain this?

Your cellphone battery can be thought of as being composed of atoms. You have the same number of atoms before and after charging it, but their arrangement is different. The differing arrangements of atoms have different energies. This translates to a difference in rest masses. Important to this argument is that the cellphone's momentum is zero before and after charging it, which is a necessary condition for the formula E=mc^2 to work. If the momentum wasn't zero, one would need the more general formula

E^2 = (mc^2)^2 + (pc)^2

where E is the Energy, m is the mass, p is the momentum, and c is the speed of light. When p=0, the more general formula reduces to E=mc^2.

To understand how the arrangement of atoms changes the energy, it is at least helpful and probably necessary to realize that energy is not just present in particles (in this case atoms), but in fields as well. We do not create or destroy atoms by charging the cellphone, but we do rearange them. At the atomic level, the chemical energy can be thought of as being associated with the electromagnetic fields that bind the atoms together.

The change in mass due to chemical binding energy is extremely small, too small for experiment to measure. Changes in mass due to changes in nuclear, rather than chemical, binding energy are large enough to be measured, though.