Electric Field Energy

Electric Field Energy:

Electric Field EnergyElectromechanical energy conversion via the electric field is analogous to the magnetic field case studied earlier. Charge in the electric field is analogous to flux linkages and voltage to current in the magnetic field case.

Figure 4.18 shows a parallel plate condenser with a fixed and a movable plate. The condenser is fed from a current source. The leakage current of the condenser is

Electric Field Energy

represented outside by conductance so that the condenser’s electric field is conservative. Let us assume that the movable plate of the condenser is held fixed in position x. The electric energy input to the ideal condenser gets stored in the electric field so that

Electric Field Energy

The capacitance C is a function of configuration (position x of the movable plate) and can be expressed as

Energy Conversion Via Electric Field

where A= plate area and co = permittivity of free space. Thus Wf, the field energy is a function of two independent variables q and x, i.e.

Energy Conversion Via Electric Field

The expression of Eq. (4.82) for the field energy immediately reveals that the electric field energy can be changed electrically by changing q or mechanically by changing x, i.e. moving the movable plate.

The field energy can also be written as

  Energy Conversion Via Electric Field

The energy density in the electric field can be expressed as

Energy Conversion Via Electric Field

where            E = electric field intensity or potential gradient

Energy Conversion Via Electric Field

Energy Conversion

Let the movable plate of the device be now permitted to move under the action of the electric field force F1 As per the principle of energy conservation:

Mechanical energy output (work done by the field force)

= electric energy input — increase in the field energy

Energy Conversion Via Electric FieldLet us choose (v, x) as independent variables. Then

Electric Field Energy

Substituting Eqs (4.86) and (4.87) in Eq. (4.85) and reorganizing

Electric Field Energy

Since v and x are independent variables, the coefficient of dv in Eq. (4.88) must be zero. Hence

Electric Field Energy

Electric Field Energy

Electric Field Energy

 

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