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What is the relative permeability of a vacuum?
1
H/m
1/4
4╧А├Ч10┬░тИТ7┬аH/m
1
Quick Summary: The relative permeability ($\mu_r$) is a dimensionless parameter that represents the ratio of the permeability of a substance to the permeability of free space (vacuum). By definition, the permeability of a vacuum ($mu_0$) is taken as the reference, thus making the relative permeability of a vacuum exactly 1.
The relative permeability (╬╝rтАЛ) is a dimensionless parameter that represents the ratio of the permeability of a substance to the permeability of free space (vacuum). By definition, the permeability of a vacuum (mu0тАЛ) is taken as the reference, thus making the relative permeability of a vacuum exactly 1.
╬╝=╬╝0тАЛ╬╝rтАЛ тАФ Relation between absolute, vacuum, and relative permeability
╬╝0тАЛ=4╧А├Ч10┬░тИТ7┬аH/m тАФ Permeability of free space
Permeability (mu) characterizes how a material responds to an external magnetic field. The relationship is defined as ╬╝=╬╝0тАЛ├Ч╬╝rтАЛ. Since for a vacuum, ╬╝=╬╝0тАЛ, it follows mathematically that ╬╝rтАЛ=╬╝0тАЛ╬╝0тАЛтАЛ=1.
Relative permeability is a dimensionless scalar quantity.
For diamagnetic materials, ╬╝rтАЛ<1 (slightly less than 1).
For paramagnetic materials, ╬╝rтАЛ>1 (slightly greater than 1).
For ferromagnetic materials, ╬╝rтАЛтЙл1.
Simplifies calculations in electromagnetic field theory by using constants.
Provides a standardized reference scale for comparing different magnetic materials.
Design of inductors and transformers.
Electromagnetic shielding analysis.
Magnetic circuit calculations.
The value ╬╝0тАЛ=4╧А├Ч10┬░тИТ7┬аH/m (Option D) is the absolute permeability of a vacuum, not the relative permeability.
Option B (1 H/m) is incorrect as permeability has units, whereas relative permeability is unitless.
A is correct тАФ The relative permeability of a vacuum is defined as the ratio of its own permeability to itself, which is exactly 1.
Always distinguish between absolute permeability (╬╝, units of H/m) and relative permeability (╬╝rтАЛ, dimensionless). Confusing these two is a common source of errors in competitive exams.