JEE MAIN - Physics (2025 - 2nd April Evening Shift - No. 19)
Given a charge q , current I and permeability of vacuum $\mu_{\mathrm{o}^*}$. Which of the following quantity has the dimension of momentum ?
${ }$ $q I / \mu_o$
$q^2 \mu_o I$
$q \mu_0 / I$
$\mathrm{q} \mu_{\mathrm{o}} \mathrm{I}$
Explanation
$$\begin{aligned}
& \mathrm{Q}=\mathrm{AT} \\
& \mathrm{I}=\mathrm{A} \\
& \mu_0=\mathrm{MLT}^{-2} \mathrm{~A}^{-2} \\
& \mathrm{P}=\mathrm{Q}^{\mathrm{x}} \mu_0^{\mathrm{y}} \mathrm{I}^{\mathrm{z}}=\left[\mathrm{AT}^{\mathrm{x}}\left[\mathrm{MLT}^{-2} \mathrm{~A}^{-2}\right]^{\mathrm{y}}[\mathrm{~A}]^{\mathrm{z}}\right. \\
& \mathrm{MLT}^{-1}=\mathrm{M}^{\mathrm{y}} \mathrm{~L}^{\mathrm{y}} \mathrm{~T}^{\mathrm{x}-2 \mathrm{y}} \mathrm{~A}^{-2 \mathrm{y}+\mathrm{z+x}} \\
& \text { Now; } \mathrm{y}=1 \\
& \mathrm{x}-2 \mathrm{y}=-1 \\
& -2 \mathrm{y}+\mathrm{z}=0 \\
& \therefore \mathrm{x}=\mathrm{y}=\mathrm{z}=1
\end{aligned}$$
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