Given a charge q, current I and permeability of vacuum μo. Which of the following quantity has the dimension of momentum? (a) qI/μo (b) q²μo I (c) qμ₀/I (d) qμo I

Answer: (d). [μ₀] = MLT⁻²A⁻² (from F/l = μ₀ I²/2π d), [q] = AT, [I] = A. [qμ₀ I] = AT·MLT⁻²A⁻² = MLT⁻¹ This is the dimension of momentum. So the answer is (d) qμ₀ I.

Given a charge q, current I and permeability of vacuum μo. Which of… | JEE Main 2025 (2 Apr, Shift 2)

Q15JEE Main 2025 · 2 APR · SHIFT 2Easy

Units & Dimensions

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

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Answer: (d)

$[\mu_0] = \mathrm{MLT^{-2}A^{-2}}$ (from $F/l = \mu_0 I^2/2\pi d$ ), $[q] = \mathrm{AT}$ , $[I] = \mathrm{A}$ .
$[q\mu_0 I] = \mathrm{AT}\cdot\mathrm{MLT^{-2}A^{-2}}\cdot\mathrm{A} = \mathrm{MLT^{-1}}$
This is the dimension of momentum.
So the answer is (d) $q\mu_0 I$ .

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