Answer 1:
You heard almost right: It's not
electromagnetic force as such, but electromagnetic
energy. You already know the equation: E = m
c^{2} If you take the amount of
chemical or electromagnetic energy stored in, say,
a car battery (about 45 Amphours at 12
Volts): 45 Amphours times 12 Volts = 540
Watthours = 2,000,000 Joules (roughly) and
convert that to mass (using mass =
E/c^{2}, and the definition of Joule =
kg*meter^{2}/c^{26}
kg*meter^{2}/s^{2}) /
(3*10^{8} meter/s)^{2} =
2*10^{(11)} kg = 2*10^{(14)}
g. You find that the energy stored in a car
battery adds 20 femtograms to the car. For
comparison, that's about 1/5 of the mass as a
1atom thick slice from one of your own hairs.
The gravitational force of so little mass is
immeasurably small. I chose a large example
(a car battery with a lot of energy) because this
shows how amazingly little gravity is exerted by
pure energy (whether chemical or electromagnetic).
To take another example, the total sunlight
hitting Earth at any time is 10^{17}
Watts. By the same calculations above, you find
that each second of sunshine adds only about 1
milligram of mass to Earth. All that
electromagnetic energy, and yet it causes so
little gravity!
