Question
Do permeability and relative permeability have the same dimensions?
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Answer
Magnetic permeability $(\mu)$ is the ratio of magnatic flux density (B) to the megnatising field strength (H).$\mu=\frac{\text{B}}{\text{H}}$
In CGS (centimeter-gram-second) dimension of B and H is same. Hence, magnetic permeability is dimensionless. But in SI unit, dimension of B and H is not same. Thus, permeability is not dimensionless. Relative permeability is defined as the ratio of magnetic permeability of any medium to the permeability of the vaccum. Hence, it is dimensionless. Thus, permeability and relative permeability have the same dimensions in CS system.
In CGS (centimeter-gram-second) dimension of B and H is same. Hence, magnetic permeability is dimensionless. But in SI unit, dimension of B and H is not same. Thus, permeability is not dimensionless. Relative permeability is defined as the ratio of magnetic permeability of any medium to the permeability of the vaccum. Hence, it is dimensionless. Thus, permeability and relative permeability have the same dimensions in CS system.
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