Does magnetism have any affect on gravity?
Not directly. However, two magnets weigh very slightly more when pulled apart than when stuck together, because of the energy stored in the magnetic field. In General Relativity, the most modern model of gravity, all forms of energy contribute to gravitational attraction.
That is cool! I don't understand it, but it is cool. Why do they weigh more and not less?
Einstein's famous formula: E=mc^2. this is to say that energy is mass. This means that the energy in the magnetic fields makes the system heavier.
Yes, that is true. It seems to me that if they are farther apart, the gravitational attraction (weight) would be less.
Think of this way: if you came across two magnets stuck together, would you have to expend energy to pull them apart? Of course, yes, you would have to put energy into the system to pull them apart. Therefore, the system contains more total energy when separated than when together. More energy = more gravitational attraction.
I see. So the energy in the system has increased. Is this what you meant by "heavier"? Or will the increase in gravitational field overcome the inverse square law, actually making the magnets pull harder on each other?
Gravity is extremely weak compared to EM anyway, so it has little effect on the magnets. I was only comparing the gravitational attraction of the entire system, as measured by an outside observer.
The system (two magnets stuck together) weighs slightly less than the system (similar two magnets pulled apart).
Thank you for the clarification.
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