Magnetic energy density

The electric and magnetic energy densities we, wm in free space (units erg cm-3) are defined as... 

The details of these intriguing phenomena are beyond the scope of this book, but the interested reader is referred to Additional Reading for further details. What is important here is to appreciate how these phenomena can and have been exploited to increase magnetic energy density by an order of magnitude for every decade since the turn of the last century ... 

Due to a high magnetic energy density, MRF can apply very high shear stresses and consequently transmit high forces. ERF are thereby... 

For the optical field, the electric and magnetic energy densities are equal so that the total electromagnetic energy density can be written as Fopt — E D/4ir. It has been shown that SmC is nearly uniaxial with the optical axis along ft, Using the uniaxial dielectric tensor ... 

Similarly, the magnetic energy density of the dc magnetic field can be written as... 

It must be stressed that, unlike our expansion of Eq. [30], which is valid only for vanishingly small values of the order parameter, Eqs. [38] and [39] are valid for arbitrary values of the order parameter. In fact, the magnetic and electric energy density expressions of the elastic continuum theory (Eqs. [3] and [4] of Chapter 8) are special cases of Eqs. [38] and [39]. For example, consider the magnetic energy density of the low temperature, anisotropic phase of a system in which only spatial variation of ri(r) is important. S f) in Eq. [38] can then be replaced by its equilibrium value , where < > denotes thermal averaging. The term proportional to H can be neglected because of its spatial invariance, and one obtains Eq. [3] of Chapter 8 directly. 

In optimizing the coil design, we will be interested in maximizing the magnetic energy density produced by the coil per unit total power consumed. 

Similar considerations for the magnetic field yield a magnetic energy density term // , given by... 

The results to be derived in this text will use the notation Xa when working in cgs units. For example, one possibility for the general magnetic energy density may be given by the analogue of the result in equation (2.98) when the contribution — PqIP is disregarded, namely. 

To this must be added the appropriate magnetic energy density. Since we are considering a semi-infinite sample, it is convenient in this situation to choose the form of magnetic energy provided by equation (2.108), giving... 

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