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I learned matter with an electric current weighs more than matter with no current. Does that apply to magnetic material in the same way but with it's magnetic fields instead of electric current? A magnet stops working over time does that mean its lost it's magnetic energy or is it a matter of realignment?

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  • $\begingroup$ Are these two questions related or separate? And I'm curious where did you learn matter with an electric current weighs more? $\endgroup$ – user115350 May 29 '16 at 5:13
  • $\begingroup$ @user115350 I learned it here. $\endgroup$ – Muze May 31 '16 at 5:32
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The answer to your question is, to a minute degree, is yes, since the total energy of something measures its source strength / coupling to gravity. So, if an system has energy $\Delta E$ added to it, it will weigh more - its gravitational mass will increase by $\Delta E/c^2$.

Practically, the effect is almost unmeasurable; a magnet's stored magnetic energy density is $\frac{1}{2}\,\mu_0\,|\vec{M}|^2$, where $\vec{M}$ is the magnetization. A quick search tells me that strong modern magnetics (e.g. Neodymium Boron ones) can be magnetized to of the order of $10^6 {\rm A\,m^{-1}}$. Thus a magnetized block of such a material with a one liter volume (that's a really chunky magnet) contains magnetic energy

$$\frac{1}{2}\,\mu_0\,|\vec{M}|^2\,V = \frac{1}{2}\times 4\,\pi\times10^{-7}\times 10^{12} \times 0.1^{-3} \approx 630\,{\rm J}$$

corresponding to an increase in gravitational mass of $630/c^2\approx 7\times 10^{-15}{\rm kg}$.

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