It has been known for a long time that such fields have mass. I believe it was derived from Maxwell's equations in the late 19th century. A more detailed explanation can be found in the Feynman lectures on physics, volume 2, chapter 28, titled "Electromagnetic mass", and elsewhere online. I'd post a link, but I can't, since I just joined the forum.
The modern view is that of relativity, where E =mc². The older electromagnetic mass derivation was E = (4/3)mc², if I remember correctly.
The modern view is that of relativity, where E =mc². The older electromagnetic mass derivation was E = (4/3)mc², if I remember correctly.