An electromechanical system in which electric energy storage is in electric fields can be analyzed by techniques directly analogous to those derived in this chapter for magnetic field systems. Consider such a system in which it is possible to separate the loss mechanism mathematically from those of energy storage in electric fields. Then the system can be represented as in figure. For a single electric terminal, Eq. 3.11 applies, where d W_elec = vi dt = v dq where v is the electric terminal voltage and q is the net charge associated with electric energy storage. Thus, by analogy to Eq. 3.16, d W_fld = v dq ? f_fld dx

a. Derive an expression for the electric stored energy Wild (q, x) analogous to that for the magnetic stored energy in Eq. 3.18.

b. Derive an expression for the force of electric origin f_fld analogous to that of Eq. 3.26. State clearly which variable must be held constant when the derivative is taken?

c. By analogy to the derivation of Eqs. 3.34 to 3.41 derive an expression for the co-energy W_fld?(v, x) and the corresponding force of electric origin.

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fna i, q Lossless electric energy storage system Mechanical terminal Electric terminal