The dimensions of permeability of free space | vedclass

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Question

(A) The force per unit length $(F/l)$ between two parallel current-carrying conductors is given by the formula:$F/l = \frac{\mu_0}{4\pi} \frac{2I_1 I_

Vedclass · Accepted Answer

$[MLT^{-2} A^{-2}]$

Vedclass · Answer

(A) The force per unit length $(F/l)$ between two parallel current-carrying conductors is given by the formula:$F/l = \frac{\mu_0}{4\pi} \frac{2I_1 I_2}{d}$Rearranging for $\mu_0$:$\mu_0 = \frac{F \cdot d}{l \cdot 2I_1 I_2}$Substituting the dimensions:$[F] = [MLT^{-2}]$$[d] = [L]$$[l] = [L]$$[I] = [A]$$[\mu_0] = \frac{[MLT^{-2}] \cdot [L]}{[L] \cdot [A]^2} = [MLT^{-2} A^{-2}]$Thus, the dimensions of permeability of free space are $[MLT^{-2} A^{-2}]$.

Column-$1$	Column-$2$
$(a)$ Wave vector	$(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density	$(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave	$(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient	$(iv)$ $M^1L^{-1}T^0$

The dimensions of permeability of free space $(\mu_0)$ can be given by:

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Match Column-$1$ with Column-$2$.
Column-$1$ Column-$2$
$(a)$ Wave vector $(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density $(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave $(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient $(iv)$ $M^1L^{-1}T^0$

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