Question

What is the formula for relative permittivity in terms of permittivity?

Answer 1

Relative permittivity, often denoted as \(\varepsilon_r\), is a dimensionless measure of how much a material can polarize in response to an electric field relative to the vacuum permittivity. It quantifies how much more or less permittivity a material has compared to the permittivity of free space (vacuum permittivity, \(\varepsilon_0\)).

### Formula for Relative Permittivity

The formula for relative permittivity (\(\varepsilon_r\)) in terms of permittivity (\(\varepsilon\)) is:

\[
\varepsilon_r = \frac{\varepsilon}{\varepsilon_0}
\]

where:
- \(\varepsilon_r\) = Relative permittivity (also known as the dielectric constant)
- \(\varepsilon\) = Absolute permittivity of the material (the permittivity of the medium)
- \(\varepsilon_0\) = Permittivity of free space (vacuum permittivity), which is a constant value approximately equal to \(8.854 \times 10^{-12} \, \text{F/m}\) (farads per meter)

### Explanation

1. **Absolute Permittivity (\(\varepsilon\))**: This is the permittivity of a material in an electric field. It describes how an electric field affects and is affected by a dielectric medium.

2. **Vacuum Permittivity (\(\varepsilon_0\))**: This is the permittivity of free space or a vacuum. It is the baseline value used for comparison when determining the relative permittivity of a material.

3. **Relative Permittivity (\(\varepsilon_r\))**: This is the ratio of the permittivity of a material (\(\varepsilon\)) to the permittivity of a vacuum (\(\varepsilon_0\)). Since it is a ratio, it is dimensionless.

### Interpretation

- If \(\varepsilon_r = 1\), the material behaves like a vacuum (air and some gases under normal conditions have \(\varepsilon_r \approx 1\)).
- If \(\varepsilon_r > 1\), the material is more polarizable than a vacuum, meaning it can store more electric energy in an electric field than a vacuum.
- The higher the \(\varepsilon_r\), the better the material acts as a dielectric, which is crucial in designing capacitors, insulators, and other electronic components.

### Example

For a material like water, the relative permittivity \(\varepsilon_r\) is approximately 80 at room temperature. This means that water has 80 times the ability to permit electric field lines compared to a vacuum.

I hope this provides a clear understanding of the formula for relative permittivity in terms of permittivity! If you have any further questions or need more examples, feel free to ask.

Answer 2

Relative permittivity, also known as the dielectric constant, is a dimensionless quantity that describes how much a material can increase the capacitance of a capacitor compared to a vacuum.

The formula for relative permittivity (εr) in terms of permittivity (ε) is:

εr = ε / ε0

where:
- ε is the absolute permittivity of the material.
- ε0 is the permittivity of free space (vacuum), which is approximately 8.854 x 10^-12 F/m (farads per meter).