Given a charge q, current I and permeability of vacuum . Which of the following quantity has the dimension of momentum? [2025]

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Solution

Q.
Given a charge q, current I and permeability of vacuum $μ_{0}$ . Which of the following quantity has the dimension of momentum [2025]

1 $q I / μ_{0}$

2 $q μ_{0} I$

3 $q^{2} μ_{0} I$

4 $q μ_{0} / I$

Ans.
(2)

Momentum = mv

$r = \frac{m v}{q B}$

$[m v] \equiv [q B r] \Rightarrow [m v] \equiv [q \frac{μ_{0} I}{2 π r} r]$

$\Rightarrow [m v] \equiv [q μ_{0} I]$

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