Q121 / 160 · AP EAMCET 2024 (23 May Shift 1) · Physics

Which of the following is not a unit of permeability

  • A
    Henry meter-1
  • B
    Weber ampere ${ }^{-1}$ meter $^{-1}$
  • C
    Ohm second meter ${ }^{-1}$
  • Correct answer
    D
    Volt second meter ${ }^{-1}$

Solution

Self inductance, $\mathrm{L}=\frac{\mu_0 \mathrm{~N}^2 \mathrm{~A}}{1}$ $\therefore \quad$ Unit of $\mu_{\mathrm{o}}=\frac{\mathrm{H} \cdot \mathrm{m}}{\mathrm{m}^2}=\mathrm{H} \mathrm{m}^{-1}$ Also, $\mathrm{L}=\frac{\phi}{\mathrm{I}}=\mathrm{WbA}^{-1}$ $\therefore \quad$ Unit of $\mu_{\mathrm{o}}=\frac{\mathrm{WbA}^{-1} \cdot \mathrm{~m}}{\mathrm{~m}^2}=\mathrm{WbA}^{-1} \mathrm{~m}^{-1}$ Also, $\mathrm{L}=\frac{\mathrm{e}}{\frac{\mathrm{dI}}{\mathrm{dt}}}=\frac{\mathrm{V}}{\mathrm{As}^{-1}}=\mathrm{VA}^{-1} \mathrm{~s}=\Omega \mathrm{s}$ $\therefore \quad$ Unit of $\mu_0=\frac{\mathrm{VsA}^{-1} \cdot \mathrm{~m}}{\mathrm{~m}^2}=\mathrm{VsA}^{-1} \mathrm{~m}^{-1}$ $=\frac{\Omega \mathrm{s} \cdot \mathrm{m}}{\mathrm{m}^2}=\Omega \mathrm{sm}^{-1}$

Hence, the correct answer is option: 'D'.

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