Yes, but that effect is very tiny. Let's say you have a lab magnet that fills 1000 cm
3 of space with a very high field of 10
5 G. That field has an energy of (roughly) 10
12 ergs. That corresponds to a mass of 10
-9 grams. So for most purposes we just forget about it.
Mike W.
(published on 08/04/2012)