The dimensional formula of permeability of fr | vedclass

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(A) The force per unit length between two parallel current-carrying wires is given by the formula: $F/l = \frac{\mu_0 I_1 I_2}{2\pi r}$.Rearranging fo

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$M^1 L^1 T^{-2} A^{-2}$

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(A) The force per unit length between two parallel current-carrying wires is given by the formula: $F/l = \frac{\mu_0 I_1 I_2}{2\pi r}$.Rearranging for $\mu_0$,we get: $\mu_0 = \frac{2\pi r F}{l I_1 I_2}$.The dimensional formula for force $F$ is $[M^1 L^1 T^{-2}]$.The dimensional formula for length $l$ is $[L^1]$.The dimensional formula for current $I$ is $[A^1]$.The dimensional formula for distance $r$ is $[L^1]$.Substituting these into the formula: $[\mu_0] = \frac{[L^1] [M^1 L^1 T^{-2}]}{[L^1] [A^1] [A^1]}$.Simplifying the expression: $[\mu_0] = [M^1 L^1 T^{-2} A^{-2}]$.

The dimensional formula of permeability of free space $\mu_0$ is

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