Using mass (M), length (L), time (T), and electric current (A) as fundamental quantities, the dimensions of magnetic permeability are:

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NEET Physics QUESTION #7222

Question 1

Using mass ($M$), length ($L$), time ($T$), and electric current ($A$) as fundamental quantities, the dimensions of magnetic permeability are:

$[M^1L^1T^{-2}A^{-2}]$
$[ML^{-2}T^{-2}A^{-1}]$
$[MLT^{-2}A^{-2}]$✔️
$[MLT^{-1}A^{-1}]$

Correct Answer Explanation

Magnetic permeability $\mu_0$ appears in: $F = \dfrac{\mu_0}{4\pi}\dfrac{I_1 I_2 l}{r}$

$[\mu_0] = \dfrac{[F][r]}{[I]^2[l]} = \dfrac{MLT^{-2} \cdot L}{A^2 \cdot L} = MLT^{-2}A^{-2}$

Alternatively, from $B = \mu_0 H$: $[H] = AL^{-1}$, $[B] = MT^{-2}A^{-1}$, so $[\mu_0] = \frac{[B]}{[H]} = \frac{MT^{-2}A^{-1}}{AL^{-1}} = MLT^{-2}A^{-2}$

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