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The magnetic energy per volume is equal to

*u=*

*1/2*μ*H*

^{2}.Say I've got an electron at rest, then the energy of the magnetic field is zero. OK.

If I give it a push so it reaches an arbitrary velocity, then it will set up a magnetic field in space, which requires some energy to create according to the formula above.

Will the electron require some extra energy other than the kinetic energy to be put in motion? If so, why isnt it mentioned anywhere and is it significant? And if not, where does it get the energy from? The electric field? Or is the answer in neither category?

I tried asking my lecturers about this, but they didnt know the answer. I also tried to find the total field energy of ∫

*u dV*over space, but I got a diverging integral since I treated the electron as a point particle... It was however dependent on the square of velocity, so it could somehow be "merged" into 1/2*m*v

^{2}. But this whole thing strikes me as odd and a bit out of place, so I would be happy if someone could clear it up.