SaM - MEMORIZE (Electrostatics)

List of things to memorize:

SaM - Electrostatics

• SaM - Electric Permittivity • Electric Susceptibility • Electric Field
• SaM - Special Materials for the Electric Permittivity • Paraelectric, Piezoelectric, Ferroelectric
• SaM - Pyroelectric Effect
• SaM - Complex Electric Permittivity
• SaM - Dielectric Materials (Skip)

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SaM - Electric Permittivity • Electric Susceptibility • Electric Field:\begin{array}{l}\text{Isotropic}:& \vec D = \kern1px\varepsilon \kern1px \vec E \\ \text{Anisotropic}:& \vec D = \overline{\overline{\varepsilon}} \vec E \end{array}$$$$\varepsilon = \varepsilon_0 \kern2px \varepsilon_r$$$$\varepsilon_0 = 8.85 \times 10^{-12} \, {\text{C}^2 \text{m}^2 \over \text{N}}$$$$\varepsilon_r = 1 + \mathcal{X}$$$$\vec D = \varepsilon_0 \vec E + \vec P$$$$\vec P = \varepsilon_0 \mathcal{X} \vec E For Air, Water and PZT (Lead Zirconate Titanate):

• ${\epsilon }_{r_{\text{AIR}}}\approx 1$
• ${\epsilon }_{r_{\text{WATER}}}\approx 80$ (@ $20°\text{C}$)
• ${\epsilon }_{r_{\text{PZT}}}\in [500÷6000]$
• Also remember that in general: ${\epsilon }_r\in [1÷6000]$.
• Terminology:
• $\epsilon$ : electric permittivity $(\epsilon ={\epsilon }_0{\epsilon }_r)$
  • ${\epsilon }_0$ : electric permittivity of the void $\left({\epsilon }_0=8.85\cdot 10^{-12}\frac{{\text{C}}^2{\text{m}}^2}{\text{N}}\right)$
  • ${\epsilon }_r$ : relative electric permittivity
• $D$ : electric displacement field $\left(D=\epsilon E\right)$
• $E$ : electric field $\left(\left[E\right]=\frac{\text{V}}{\text{m}}\right)$
• $P$ : polarization vector $\left(P={\epsilon }_0\mathcal{X}E\right)$
• $\mathcal{X}$ : electric susceptibility $\left({\epsilon }_r=1+\mathcal{X}\right)$
• Si : Silicon.
• PZT : Lead Zirconate Titanate.

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SaM - Special Materials for the Electric Permittivity • Paraelectric, Piezoelectric, Ferroelectric: Paraelectric Materials:

Pyroelectric Materials:

Ferroelectric Materials:

Pyroelectric Materials, pyroelectric effect:

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SaM - Complex Electric Permittivity:$\hat{\epsilon }={\epsilon }^{\prime }-j{\epsilon }^{\prime \prime }$Static description:${\epsilon }_{DC}={\lim }_{\omega \to 0}\hat{\epsilon }(\omega )$ Examples:

• ~Ex.: Water: ${\epsilon }^{\prime }=78.5$, ${\epsilon }^{\prime \prime }=2.25$ ⇒ $\frac{{\epsilon }^{\prime \prime }}{{\epsilon }^{\prime }}\gg 1$.
  • So it’s a good conductor, but a poor dielectric (waves do not propagate well).
• ~Ex.: Vacum: ${\epsilon }^{\prime }=1$, ${\epsilon }^{\prime \prime }=0$ ⇒ $\frac{{\epsilon }^{\prime \prime }}{{\epsilon }^{\prime }}=0$.
  • So it’s a perfect dielectric, waves do not attenuate, but does not conduct electricity, at all.

Ratio table:

• Terminology:
  • ${\epsilon }_{DC}$ : static electric permittivity $\left({\epsilon }_{DC}={\lim }_{\omega \to 0}\hat{\epsilon }(\omega )\right)$
  • $\hat{\epsilon }$ : complex electric permittivity $\left(\hat{\epsilon }={\epsilon }^{\prime }-j{\epsilon }^{\prime \prime }\right)$
    • ${\epsilon }^{\prime }$ : real electric permittivity (represents the material’s ability to store energy as an electric field)
    • ${\epsilon }^{\prime \prime }$ : imaginary electric permittivity (represents the material’s ability to dissipate energy as heat when subjected to an alternating electric field)

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SaM - Dielectric Materials (Skipped)