Relative permeability of vacuum is:

Explanation:

Relative Permeability of Vacuum

Definition: Relative permeability is a dimensionless measure of the permeability of a material relative to the permeability of free space (vacuum). It is denoted by the symbol μ_r. The permeability of free space, also known as the vacuum permeability, is a physical constant denoted by μ₀.

Understanding Permeability: Permeability is a property of a material that describes the ability of the material to support the formation of a magnetic field within itself. In simpler terms, it indicates how much a material can become magnetized when exposed to an external magnetic field.

Vacuum Permeability (μ₀): The permeability of vacuum is a fundamental physical constant used in electromagnetism. It has a precise value given by:

μ₀ = 4π × 10^-7 H/m (Henries per meter)

This value is crucial in the formulation of Maxwell's equations, which describe the behavior of electric and magnetic fields.

Relative Permeability (μ_r): Relative permeability is defined as the ratio of the permeability of a material (μ) to the permeability of free space (μ₀):

μ_r = μ / μ₀

For a vacuum, the permeability is μ₀ itself. Therefore, the relative permeability of vacuum is:

μ_r = μ₀ / μ₀ = 1

Hence, the relative permeability of vacuum is 1. This implies that vacuum does not enhance or diminish the magnetic field, maintaining it as it is.

Correct Option Analysis:

The correct option is:

Option 3: 1

This option correctly represents the relative permeability of vacuum, which is a dimensionless quantity equal to 1.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 4π × 10^-7 H/m

This option represents the absolute permeability of vacuum (μ₀), not the relative permeability. While 4π × 10^-7 H/m is the correct value for μ₀, it is not the relative permeability, which is a dimensionless number.

Option 2: 1 H/m

This option is incorrect because it suggests a value with units of Henries per meter (H/m). Relative permeability is a dimensionless quantity, not one with units. Therefore, this option is not valid.

Option 4: 1/4π H/m

This option is incorrect as it presents a value with units of Henries per meter (H/m) and suggests an inverse relationship with π. The relative permeability of vacuum is a simple dimensionless ratio and should not have any units or involve π in its expression.

Conclusion:

Understanding the concept of relative permeability and the specific properties of vacuum permeability is crucial for accurately interpreting and applying these physical constants in electromagnetism. The relative permeability of vacuum is a fundamental concept indicating that vacuum does not alter the magnetic field passing through it, maintaining it as it is, with a value of 1. This basic understanding is essential for studying and working with electromagnetic fields and materials in various scientific and engineering applications.