Waite short note on Magnetic energy.
Answers
Answer:
Magnetic energy and electrostatic potential energy are related by Maxwell's equations. The potential energy of a magnet or magnetic moment {\displaystyle \mathbf {m} } {\mathbf {m}} in a magnetic field {\displaystyle \mathbf {B} } \mathbf {B} is defined as the mechanical work of the magnetic force (actually magnetic torque) on the re-alignment of the vector of the magnetic dipole moment and is equal to:
{\displaystyle E_{\rm {p,m}}=-\mathbf {m} \cdot \mathbf {B} } {\displaystyle E_{\rm {p,m}}=-\mathbf {m} \cdot \mathbf {B} }
while the energy stored in an inductor (of inductance {\displaystyle L} L) when a current {\displaystyle I} I flows through it is given by:
{\displaystyle E_{\rm {p,m}}={\frac {1}{2}}LI^{2}.} {\displaystyle E_{\rm {p,m}}={\frac {1}{2}}LI^{2}.}
This second expression forms the basis for superconducting magnetic energy storage.
Energy is also stored in a magnetic field. The energy per unit volume in a region of space of permeability {\displaystyle \mu _{0}} {\displaystyle \mu _{0}} containing magnetic field {\displaystyle \mathbf {B} } \mathbf {B} is:
{\displaystyle u={\frac {1}{2}}{\frac {B^{2}}{\mu _{0}}}} {\displaystyle u={\frac {1}{2}}{\frac {B^{2}}{\mu _{0}}}}
More generally, if we assume that the medium is paramagnetic or diamagnetic so that a linear constitutive equation exists that relates {\displaystyle \mathbf {B} } \mathbf {B} and {\displaystyle \mathbf {H} } \mathbf{H}, then it can be shown that the magnetic field stores an energy of
{\displaystyle E={\frac {1}{2}}\int \mathbf {H} \cdot \mathbf {B} \ \mathrm {d} V} {\displaystyle E={\frac {1}{2}}\int \mathbf {H} \cdot \mathbf {B} \ \mathrm {d} V}
where the integral is evaluated over the entire region where the magnetic field exists.[
Answer:
Each magnetic field contains energy, also called magnetic energy. She is a constant in physics. Because a magnetic field is generated by electric currents, the magnetic energy is an energy form of moving charge carriers (electrons).
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