Stupid question on energy

1. Feb 28, 2015

HummusAkemi

I pry two magnets apart. The magnets attract each other. Say they exert a constant force F on each other. I exert an equivalent force F on each in the opposite direction and pull them apart a distance d (pull each of them d/2 distance). So I have done positive work Fd in total and increased the potential energy of the arrangement by Fd. The magnets have each done negative work -Fd/2 on each other.
Me: lost Fd energy
Left magnet: lost Fd/2 energy from work done on other magnet
Right magnet: lost Fd/2 energy from work done on other magnet
The potential energy of the arrangement rose by Fd.

Anyone tell me where I messed up? Because conservation of energy doesn't work out.

2. Mar 1, 2015

Simon Bridge

The magnets have not lost any energy - you have done work storing energy in the magnetic field between the magnets.
The amount of energy stored is the same as the work you did.

3. Mar 1, 2015

Delta²

Τhe middle statements about the left and right magnet are wrong. The left magnet doesnt lose Fd/2 energy instead it gains Fd/2 potential energy. Similar right magnet gains Fd/2 potential energy. It is a gain in potential energy rather than a gain in kinetic energy that we would have if there was no magnetic field. You view that "possible" gain in kinetic energy as a loss which isnt realy an energy loss, it is a gain in potential energy instead.

4. Mar 1, 2015

HummusAkemi

Thanks, you two. Ok, I think I get it now