Which of the following is not a unit of perme | vedclass

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(D) The permeability of free space $\mu_0$ has the $SI$ unit of Henry per meter $(H \cdot m^{-1})$.From the formula for self-inductance $L = \frac{\mu

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Volt second meter$^{-1}$

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(D) The permeability of free space $\mu_0$ has the $SI$ unit of Henry per meter $(H \cdot m^{-1})$.From the formula for self-inductance $L = \frac{\mu_0 N^2 A}{l}$,we get the unit of $\mu_0$ as $\frac{H \cdot m}{m^2} = H \cdot m^{-1}$. Thus,option $A$ is a unit.Since $L = \frac{\phi}{I}$,the unit of $L$ is $Wb \cdot A^{-1}$. Substituting this into the expression for $\mu_0$,we get $\frac{Wb \cdot A^{-1} \cdot m}{m^2} = Wb \cdot A^{-1} \cdot m^{-1}$. Thus,option $B$ is a unit.Since $L = \frac{e}{dI/dt}$,the unit of $L$ is $\frac{V}{A \cdot s^{-1}} = V \cdot s \cdot A^{-1} = \Omega \cdot s$. Substituting this into the expression for $\mu_0$,we get $\frac{\Omega \cdot s \cdot m}{m^2} = \Omega \cdot s \cdot m^{-1}$. Thus,option $C$ is a unit.Option $D$ $(Volt \cdot second \cdot meter^{-1})$ is equivalent to $V \cdot s \cdot m^{-1}$. Comparing this with the derived units,it lacks the $A^{-1}$ factor required for permeability. Therefore,it is not a unit of permeability.

Which of the following is not a unit of permeability?

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