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Asked by Mohd Last Modified
Answer 
YES; they most certainly do. I am giving you a very brief conceptual answer, without equations for starter.
consider an EM field. Now if you are to carry a point charge from infinity(field =0) to a certain point, you need to do some work against it, which will be stored as energy in the field. Now in a static configuration, there is no EM wave. But consider, some of the energy stored is flowing out of a small volume, then that will constitue as EM wave, which will be carrying off the above mentioned energy. similarly, they also carry the moentum, though the argument is bit different.
a very interesting example of EM waves carrying momentum is Feynmann Disk paradox. You can look it up,or contact me.
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