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Given a charge q, current I and permeability of vacuum μ₀. Which of the following quantity has the dimension of momentum?

Asked in JEE Main 2nd April 2nd Shift 2025 · Pairs with the same dimensions

(1) (qI)/(μ₀)
(2) qμ₀I
(3) (qμ₀)/I
(4) q²μ₀I

Answer: (2) qμ₀I

Step-by-step solution

Given: q=[TA], I=[A], μ₀=[MLT⁻²A⁻²].

Test qμ₀I:

[TA][MLT⁻²A⁻²][A]=[MLT⁻¹A⁰].

[MLT⁻¹] is exactly momentum, so the answer is qμ₀I.

Why the other options are wrong

(1) comes from divides by the permeability, which inverts the mass and length exponents
(3) comes from divides by the current, leaving a stray A⁻²
(4) comes from squares the charge, leaving a stray TA

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