## Momentum Stored inside an Electromagnetic Field

Quite a vague question here, and I'm not entirely sure I'll be able to get a satisfying answer out of this one, but here goes.

Fields such as the electric or magnetic field are introduced as vector fields that allow you to calculate a force at a certain point in space. In this interpretation they are conceptually on exactly the same footing as an 'action at a distance' theory such as Newton's gravity.

However, as you progress in electrodynamics, you learn that the fields have energy and momentum stored inside them. Now I understood how energy could be stored in a certain charge configuration (and thus it could be modeled as 'stored inside of the field'). But the idea of the electromagnetic field having a certain amount of momentum seemed bizarre to me. Does this mean I have to abandon the idea of the field being something purely mathematical altogether, or is there some sort of analogy or explanation that can help me understand it?

Thanks.

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 Recognitions: Gold Member Yeah, I suppose it does sound a bit strange at first - but then again, photons have momentum so it makes sense that the EM field should as well. If we have two changes q and q' separated by some distance and we shove q towards q' then the force on q will increase immediately but the increase in the force on q' will happen some time later (after the EM wave has travelled the distance between the two particles). It's like the action and reaction forces are out of balance as there's a force pushing back on q reducing the momentum but for a while there's no corresponding force on q' to increase this particle's momentum. If we want momentum to be conserved then I think we have to admit that the missing momentum has been temporarily transferred to the field. The same sort of thing goes for energy - a beam of light moves energy from place to place and you can imagine how the conservation of energy principle requires the EM field to have energy. I'd say that the field exists as a thing in its own right - if it didn't then we could come up with examples where momentum and energy weren't conserved.

 Quote by BVM Quite a vague question here, and I'm not entirely sure I'll be able to get a satisfying answer out of this one, but here goes. Fields such as the electric or magnetic field are introduced as vector fields that allow you to calculate a force at a certain point in space. In this interpretation they are conceptually on exactly the same footing as an 'action at a distance' theory such as Newton's gravity. However, as you progress in electrodynamics, you learn that the fields have energy and momentum stored inside them. Now I understood how energy could be stored in a certain charge configuration (and thus it could be modeled as 'stored inside of the field'). But the idea of the electromagnetic field having a certain amount of momentum seemed bizarre to me. Does this mean I have to abandon the idea of the field being something purely mathematical altogether, or is there some sort of analogy or explanation that can help me understand it? Thanks.
Yes, I guess you have to. Everything becomes more and more bizarre as you progress. Oscillating EM field gives off light, which is something physical, it is not purely mathematical anymore.

## Momentum Stored inside an Electromagnetic Field

 Quote by MalachiK Yeah, I suppose it does sound a bit strange at first - but then again, photons have momentum so it makes sense that the EM field should as well. If we have two changes q and q' separated by some distance and we shove q towards q' then the force on q will increase immediately but the increase in the force on q' will happen some time later (after the EM wave has travelled the distance between the two particles). It's like the action and reaction forces are out of balance as there's a force pushing back on q reducing the momentum but for a while there's no corresponding force on q' to increase this particle's momentum. If we want momentum to be conserved then I think we have to admit that the missing momentum has been temporarily transferred to the field. The same sort of thing goes for energy - a beam of light moves energy from place to place and you can imagine how the conservation of energy principle requires the EM field to have energy. I'd say that the field exists as a thing in its own right - if it didn't then we could come up with examples where momentum and energy weren't conserved.
Thanks! That answer really helped me understand the problem.

Recognitions:
 Quote by BVM Quite a vague question here, and I'm not entirely sure I'll be able to get a satisfying answer out of this one, but here goes.
The momentum of an electromagnetic field is defined as the Poynting vector S = E × H. Note that for propagating fields, that's proportional to the wavevector.