# Electric versus Magnetic Field Energy

The field energy in joules per cubic meter, and the pressure of the field in pascals, are equivalent (in vacuum). Compressing a constant energy field by one cubic meter is equivalent to pushing a square meter of the side by one meter against the pressure in pascals.

The energy density of a magnetic field in vacuum is the flux density squared divided by 2 times the free space permeability. For a 1.6 Tesla field (the maximum practical field with copper wound around an iron core), and a permiability of 4π&mult;1E-7, that is about one megajoule per cubic meter.

The energy density of an electrical field in vacuum is quite a bit lower. The maximum practical electrical field is about 1 megavolt per meter, though an arc breakdown can easily get started that keeps going until it vaporizes the electrodes. The field energy is the field squared times half the permittivity of free space, 8.85E-12 farads per meter, for an energy density of 4 joules per cubic meter. This is more than 5 orders of magnitude smaller than the magnetic field.

Solid capacitors with high dielectric constants can store significantly more energy, though not as much as a magnetic field can. Dielectrics increase the energy stored in the field (because the permittivity increases), while ferromagnetic material increases the permiability and *decreases* the magnetic energy density. This means that most of the energy in a magnetic circuit is stored in air gaps. That makes magnetic motors and solenoids a lot more powerful at the millimeter to meter scale.

At the molecular scale, electrostatic fields can store more energy, because of the potential energy needed to pull loose an electron prevents arcs and permits much higher electric fields than a million volts per meter. Two molecules spaced a nanometer apart, with a 1 volt field between them, will have a very high energy density in the tiny space between them. This is important for the microscopic behavior of materials. At the meter scale. other effects take place.

With a million volt field between two plates a meter apart, if one electron or ionized gas molecule finds its way into the gap, it will be accelerated towards the oppositely charged plate with up to a million electron volts of energy. With typical chemical bonds around one to five electron volts, the arrival of this particle can disrupt thousands of chemical bonds, kicking loose many ionized atoms and electrons. They will in turn accelerate towards the oppositely charged plate, and kick loose far more particles. Very soon, there will be an avalanche of charged particles filling the space between the plates, increasing the density until the plates are vaporized or the power supply fails.

In vacuum, voltages larger than 200V can lead to sustained arcing under some conditions. However, fields of 10V per micrometer may be practical at the micrometer scale. For a 100 micrometer thread with a density of 3, the mass density is 20 milligrams per meter while the acceleration is be on the order of 200 meters per second squared. This is the same acceleration as a magnetic field on a slab of iron 30 centimeters thick (2500 kg/m^{2}) in a 1.6 tesla field. In both cases, the turning radius moving at 10 km/sec is 500 kilometers. If the slab is a meter wide, it stores 1.25E11 joules per meter (about $2000 worth of electricity). The thread stores about 1E3 joules per meter.

So for very small structures like thin threads, electric fields can provide significant force. Further, since individual charged carriers can be emitted across space to the thread, this permits control of threads by distant particle sources. However, for large systems weighing many kilograms per meter, magnetic fields are the only practical way to transmit large forces across a vacuum gap.