WHAT IS ELECTRICAL PERMITTIVITY? (WITH EXPERIMENT) - PHYSICAL - 2025

The electric permittivity is the parameter that quantifies the response of a medium in the presence of an electric field. It is denoted by the Greek letter ε and its value for vacuum, which serves as a reference for the other media, is the following: ε _o = 8.8541878176 x 10 ^-12 C ² / Nm ²

The nature of the medium gives it a particular response to electric fields. In this way, temperature, humidity, molecular weight, the geometry of the constituent molecules, the mechanical stresses in the interior influence, or that there is some preferential direction in the space in which the existence of the field is facilitated.

Figure 1. Air becomes conductive above a certain voltage. Source: Pixabay.

In the latter case, the material is said to have anisotropy. And when neither direction is preferential the material is considered isotropic. The permeability of any homogeneous medium can be expressed as a function of the permeability of the vacuum ε _or by the expression:

ε = κε _or

Where κ is the relative permeability of the material, also called the dielectric constant, a dimensionless quantity that has been determined experimentally for many materials. A way to carry out this measurement will be explained later.

Dielectrics and Capacitors

A dielectric is a material that does not conduct electricity well, so it can be used as an insulator. However, this does not prevent the material from being able to respond to an external electric field, creating its own.

In what follows we will analyze the response of isotropic dielectric materials such as glass, wax, paper, porcelain, and some fats that are commonly used in electronics.

An electric field external to the dielectric can be created between two metallic sheets of a flat parallel plate capacitor.

Dielectrics, unlike conductors like copper, lack free charges that can move within the material. Their constituent molecules are electrically neutral, but charges can shift slightly. In this way they can be modeled as electric dipoles.

A dipole is electrically neutral, but the positive charge is a small distance away from the negative charge. Within the dielectric material and in the absence of an external electric field, the dipoles are usually randomly distributed, as shown in Figure 2.

Figure 2. In a dielectric material the dipoles are oriented randomly. Source: self made.

Dielectric in an external electric field

When the dielectric is introduced in the middle of an external field, for example the one created inside two conductive sheets, the dipoles reorganize and the charges separate, creating an internal electric field in the material in the opposite direction to the external field..

When this displacement occurs, the material is said to be polarized.

Figure 3. Polarized dielectric material. Source: self made.

This induced polarization causes the net or resultant electric field E to decrease, an effect shown in figure 3, since the external field and the internal field generated by said polarization have the same direction but opposite directions. The magnitude of E is given by:

The external field undergoes a reduction thanks to the interaction with the material in a factor called κ or dielectric constant of the material, a macroscopic property of the same. In terms of this quantity, the resulting or net field is:

The dielectric constant κ is the relative permittivity of the material, a dimensionless quantity always greater than 1 and equal to 1 in vacuum.

Either ε = κε _or as described at the beginning. The units of ε are the same as those of ε _o: C ² / Nm ² or F / m.

Measurement of electrical permittivity

The effect of inserting a dielectric between the plates of a capacitor is to allow a storage of additional charges, that is, an increase in capacity. This fact was discovered by Michael Faraday in the 19th century.

It is possible to measure the dielectric constant of a material using a flat parallel plate capacitor in the following way: when there is only air between the plates, it can be shown that the capacity is given by:

Where C _o is the capacitance of the capacitor, A is the area of ​​the plates and d is the distance between them. But when inserting a dielectric, the capacity increases by a factor κ, as seen in the previous section, and then the new capacity C is proportional to the original:

C = κε _or. A / d = ε. A / d

The ratio between the final and initial capacity is the dielectric constant of the material or relative permittivity:

κ = C / C _or

And the absolute electrical permittivity of the material in question is known through:

ε = ε _o. (C / C _o)

Measurements can be easily carried out if you have a multimeter capable of measuring capacitance. An alternative is to measure the voltage Vo between the plates of the capacitor without dielectric and isolated from the source. Then the dielectric is introduced and a decrease in voltage is observed, the value of which will be V.

Then κ = V _or / V

Experiment to measure the electrical permittivity of air

-Materials

- Adjustable spacing parallel flat plate condenser.

- Micrometric or vernier screw.

- Multimeter that has the function of measuring capacity.

- Graph paper.

-Process

- Choose a separation d between the capacitor plates and with the help of the multimeter measure the capacity C _o. Record the data pair in a table of values.

- Repeat the above procedure for at least 5 plate separations.

- Find the quotient (A / d) for each of the measured distances.

- Thanks to the expression C _o = ε _o. A / d it is known that C _o is proportional to the quotient (A / d). Plot each value of C _or its respective A / d value on graph paper.

- Visually adjust the best line and determine its slope. Or find the slope using linear regression. The value of the slope is the permittivity of air.

Important

The spacing between the plates should not exceed about 2 mm, since the equation for the capacitance of the parallel flat plate capacitor assumes infinite plates. However, this is a fairly good approximation, since the side of the plates is always much greater than the separation between them.

In this experiment, the permittivity of air is determined, which is quite close to that of a vacuum. The dielectric constant of vacuum is κ = 1, while that of dry air is κ = 1.00059.

References

1. Dielectric. Dielectric constant. Recovered from: electricistas.cl.
2. Figueroa, Douglas. 2007. Physics Series for Science and Engineering. Volume 5 Electrical Interaction. 2nd. Edition. 213-215.
3. Laboratori d'Electricitat i Magnetisme (UPC). Relative Permitivity of a Material. Recovered from: elaula.es.
4. Monge, M. Dielectrics. Electrostatic field. University Carlos III of Madrid. Recovered from: ocw.uc3m.es.
5. Sears, Zemansky. 2016. University Physics with Modern Physics. 14 ^th. Ed. 797-806.