Talk:Capacitor/deprecated sections

Displacement current

Main article: Displacement current

The physicist James Clerk Maxwell invented the concept of displacement current, dD/dt, to make Ampère's law consistent with conservation of charge in cases where charge is accumulating as in a capacitor. He interpreted this as a real motion of charges, even in vacuum, where he supposed that it corresponded to motion of dipole charges in the aether. Although this interpretation has been abandoned, Maxwell's correction to Ampère's law remains valid.

Hydraulic analogy

Main article: Hydraulic analogy

As electrical circuitry can be modeled by fluid flow, a capacitor can be modeled as a chamber with a flexible diaphragm separating the input from the output. As can be determined intuitively as well as mathematically, this provides the correct characteristics:

• The pressure difference (voltage difference) across the unit is proportional to the integral of the flow (current).
• A steady state current cannot pass through it because the pressure will build up across the diaphragm until it equally opposes the source pressure,
• but a transient pulse or alternating current can be transmitted.
• An overpressure results in bursting of the diaphragm, analogous to dielectric breakdown.
• The capacitance of units connected in parallel is equivalent to the sum of their individual capacitances.

Laplace equivalent (s-domain)

When using the Laplace transform in circuit analysis, the capacitive impedance is represented in the s domain by:

$Z(s)={\frac {1}{Cs}}$

where s = σ + jω is the Laplace-domain complex frequency.

Dielectric permittivity

The symbol ε in these equations represents the dielectric permittivity. Capacitance can be enhanced by using a dielectric with a higher permittivity value. A simple thought experiment can help explain this phenomenon. Imagine an additional metal plate inserted between z = ¼ d and z = ¾ d. Since the electric field inside solid metal is zero, the above integral becomes

$V=\int _{0}^{d}{\frac {\rho }{\varepsilon }}\mathrm {d} z-\int _{d/4}^{3d/4}{\frac {\rho }{\varepsilon }}\mathrm {d} z={\frac {Q}{\varepsilon }}{\frac {d}{2A}}$

where the negative term reflects the cancellation of the electric field by the metal. The metal accomplishes this cancellation by assuming a polarity and a dipole moment. As the voltage is halved, the capacitance is doubled. Materials with high permittivity consist of molecules with an analogous tendency to polarize. Such substances include oxides of group 4 and group 5 elements.

Duality with inductors and modeling fields

Main article: duality (electrical circuits)

Capacitors are to electric fields what inductors are to magnetic fields. Both devices store energy in a well-contained dipole force field. The current-voltage equations of the capacitor, described below, simply exchange current and voltage terms from those of the inductor. Whereas voltage indicates electric field potential, current indicates magnetic field potential.

The analogy carries over to modeling undesirable fields. Mutual capacitance describes the tendency of a changing electric field emanating from one conductor to induce a voltage change on another conductor. In a circuit, this is modeled as a capacitor connecting the conductors. It is found with its magnetic analogy, mutual inductance, in a transmission line.

Monopoles present one difference between electric and magnetic fields. However, as the observable universe has no net charge, it should be noted that all electric field lines do terminate at equal and opposite charges. The limiting behavior as the opposite capacitor plate is moved infinitely far away, and local field (containing the majority of the total energy) appears as a monopole, is called self-capacitance. In this regime, the parallel-plate distance d ceases to affect capacitance or energy.