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CGP EDU Academic Team
Published on: September 12, 2026
What is the SI unit of permeability
Text Solution
Verified by ExpertsThe correct answer is:
D
Permeability ($\mu$) is defined as the measure of the resistance of a material against the formation of a magnetic field.
Let us derive the units using various relations involving permeability:
1. In terms of Inductance:
The self-inductance of a solenoid is given by $L = rac{\mu N^2 A}{l}$, which gives $\mu = rac{L \cdot l}{N^2 A}$.
$ ext{Unit of } \mu = rac{ ext{Henry} imes ext{metre}}{ ext{metre}^2} = ext{Henry per metre } ( ext{H/m})$.
Hence, Option A is correct.
2. In terms of Magnetic Field ($B$) and Magnetic Field Strength ($H$):
$B = \mu H \implies \mu = rac{B}{H}$
Since $B$ is in Tesla ($ ext{T}$) and $H$ is in Ampere per metre ($ ext{A/m}$):
$ ext{Unit of } \mu = rac{ ext{Tesla}}{ ext{Ampere/metre}} = ext{Tesla metre per ampere } ( ext{T}\cdot ext{m}\cdot ext{A}^{-1})$.
Hence, Option B is correct.
3. In terms of Magnetic Flux ($\Phi$):
Since $1 ext{ Tesla} = 1 ext{ Weber}/ ext{metre}^2$, substituting this into the above expression:
$ ext{Unit of } \mu = rac{ ext{Weber}/ ext{metre}^2}{ ext{Ampere}/ ext{metre}} = ext{Weber per ampere metre } ( ext{Wb}\cdot ext{A}^{-1}\cdot ext{m}^{-1})$.
Hence, Option C is correct.
Therefore, all the given units are equivalent and correct.
Thus, the correct option is D.
Let us derive the units using various relations involving permeability:
1. In terms of Inductance:
The self-inductance of a solenoid is given by $L = rac{\mu N^2 A}{l}$, which gives $\mu = rac{L \cdot l}{N^2 A}$.
$ ext{Unit of } \mu = rac{ ext{Henry} imes ext{metre}}{ ext{metre}^2} = ext{Henry per metre } ( ext{H/m})$.
Hence, Option A is correct.
2. In terms of Magnetic Field ($B$) and Magnetic Field Strength ($H$):
$B = \mu H \implies \mu = rac{B}{H}$
Since $B$ is in Tesla ($ ext{T}$) and $H$ is in Ampere per metre ($ ext{A/m}$):
$ ext{Unit of } \mu = rac{ ext{Tesla}}{ ext{Ampere/metre}} = ext{Tesla metre per ampere } ( ext{T}\cdot ext{m}\cdot ext{A}^{-1})$.
Hence, Option B is correct.
3. In terms of Magnetic Flux ($\Phi$):
Since $1 ext{ Tesla} = 1 ext{ Weber}/ ext{metre}^2$, substituting this into the above expression:
$ ext{Unit of } \mu = rac{ ext{Weber}/ ext{metre}^2}{ ext{Ampere}/ ext{metre}} = ext{Weber per ampere metre } ( ext{Wb}\cdot ext{A}^{-1}\cdot ext{m}^{-1})$.
Hence, Option C is correct.
Therefore, all the given units are equivalent and correct.
Thus, the correct option is D.
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