Given a charge q,current I and permeability o | vedclass

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(B) The dimension of momentum $P$ is $[MLT^{-1}]$.Given dimensions are: $[q] = [AT]$,$[I] = [A]$,and $[\mu_0] = [MLT^{-2}A^{-2}]$.Let the dimension of

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$q \mu_0 I$

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(B) The dimension of momentum $P$ is $[MLT^{-1}]$.Given dimensions are: $[q] = [AT]$,$[I] = [A]$,and $[\mu_0] = [MLT^{-2}A^{-2}]$.Let the dimension of the quantity be $[P] = [q]^x [\mu_0]^y [I]^z$.Substituting the dimensions: $[MLT^{-1}] = [AT]^x [MLT^{-2}A^{-2}]^y [A]^z$.$[MLT^{-1}] = [M^y L^y T^{x-2y} A^{x-2y+z}]$.Comparing the powers of $M, L, T,$ and $A$ on both sides:For $M$: $y = 1$.For $L$: $y = 1$.For $T$: $x - 2y = -1 \Rightarrow x - 2(1) = -1 \Rightarrow x = 1$.For $A$: $x - 2y + z = 0 \Rightarrow 1 - 2(1) + z = 0 \Rightarrow -1 + z = 0 \Rightarrow z = 1$.Thus,the required quantity is $[q^1 \mu_0^1 I^1] = [q \mu_0 I]$.

Given a charge $q$,current $I$ and permeability of vacuum $\mu_0$. Which of the following quantity has the dimension of momentum?

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