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Question:
Derive the expression for relative permittivity ..wrt to air and vacuum.
Answer:

The relative permittivity of a material is absolute permittivity expressed as a ratio relative to the permittivity of vacuum. The physical constant ε0, commonly called the vacuum permittivity, permittivity of free space.

ε0 = 8.854 187 817... × 10−12 F·m−1 (farads per metre).

The relative permittivity of air changes with temperature, humidity, and barometric pressure. Sensors can be constructed to detect changes in capacitance caused by changes in the relative permittivity. Most of this change is due to effects of temperature and humidity as the barometric pressure is fairly stable. Using the capacitance change, along with the measured temperature, the relative humidity can be obtained using engineering formulas.

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