# How much energy is stored in a magnetic field

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#### syhprum

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##### How much energy is stored in a magnetic field
« on: 09/09/2014 20:54:53 »
In a recent discussion of gravity and magnetism it was noted that a magnetic field stores energy that has a mass equivalent.
I am weak on units but would like to know how much energy is stored per M^3 in a 1T field and whether in the intense field around a magnastar  the mass equivalent of the energy could approach that of water 1000kg/m^3
syhprum

#### PmbPhy

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##### Re: How much energy is stored in a magnetic field
« Reply #1 on: 09/09/2014 21:09:01 »
In a recent discussion of gravity and magnetism it was noted that a magnetic field stores energy that has a mass equivalent.
I am weak on units but would like to know how much energy is stored per M^3 in a 1T field and whether in the intense field around a magnastar  the mass equivalent of the energy could approach that of water 1000kg/m^3
The energy density in joules per cubit meter is given by

$$u = \frac{1}{2}\frac{B}{\mu}$$

where B is given in terms of Telsas or amps per meter, which is the same. $$\mu = 4\pi 10^{-7} H/m$$ is the permeability of free space. See http://en.wikipedia.org/wiki/Permeability_(electromagnetism)

Given this you can easily calculate the result for yourself.

#### syhprum

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##### Re: How much energy is stored in a magnetic field
« Reply #2 on: 09/09/2014 21:23:59 »
Thank you as you say I can easily calculate the rest myself the only thing I don't know is the strength of the field of the magnastar but perhaps Wiki has the answer.
syhprum

#### syhprum

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##### Re: How much energy is stored in a magnetic field
« Reply #3 on: 09/09/2014 21:56:56 »
The Wiki article on magnetar,s gives all the answers, for a typical field of 10^10 T the energy density is 4*10^25 J/M^3  , converting with e=mc^2 gives a density 10^4 times that of lead.

Incredible
syhprum

#### yor_on

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##### Re: How much energy is stored in a magnetic field
« Reply #4 on: 10/09/2014 20:28:57 »
The energy in that magnetic field was indeed impressive syphrum. You writing about magnastars made me Google And what I found was interesting, although it briefly made me wonder about gravity, as expressed by lead, and magnetism. I can't define gravity to magnetism, even though I can see the equivalence in 'energy containment' between those two, lead and a magnastars magnetic field, as you did..

found those cool links though. http://www.space.com/21347-strange-magnetar-neutron-star-glitch.html