There will be no any path for the flow of electrons. So conductivity is zero in free space

Conductivity in Free Space Medium

Conductivity is a fundamental property of a material that determines how well it can conduct electric current. In the context of this question, we are considering the conductivity of a free space medium, which refers to the vacuum or empty space.

1. Definition of Conductivity:
Conductivity is a measure of a material's ability to conduct electric current. It is the reciprocal of resistivity, which is a measure of a material's opposition to the flow of electric current. Conductivity is denoted by the symbol σ and is measured in units of siemens per meter (S/m).

2. Conductivity in Free Space:
In free space, the conductivity is zero. This means that free space does not conduct electric current. The concept of conductivity is applicable to materials that contain charged particles (such as electrons or ions) that can move freely in response to an electric field. However, free space is devoid of such charged particles, making it an insulating medium.

3. Explanation:
Free space, or vacuum, is a region that is completely devoid of matter. It does not contain any particles that can carry electric charge. In the absence of charged particles, there are no free charges available to move in response to an electric field and thus no current can flow through free space.

4. Comparison to Other Materials:
In contrast to free space, most materials have finite conductivities. Conductors, such as metals, have high conductivities due to the presence of free electrons that can move easily in response to an electric field. Insulators, on the other hand, have low conductivities as their electrons are tightly bound and cannot move freely.

5. Applications:
The concept of conductivity in free space is important in various fields of science and engineering. It is used in the analysis of electromagnetic waves, such as radio waves, microwaves, and light. In free space, these waves propagate without any loss of energy due to the absence of conductive materials that can dissipate the energy.

In conclusion, the conductivity in a free space medium is zero. Free space lacks charged particles that can move freely, making it an insulating medium. This is in contrast to most materials that have finite conductivities.