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Physics Question 27 – JEE-MAIN 2025

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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 ?

The problem requires finding a combination of given physical quantities that results in the dimensions of momentum.

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Ninja Strategy•Dimensional Consistency Check

Systematically check the dimensions of each option against the known dimensions of momentum, eliminating options that clearly do not match in terms of fundamental units like mass, length, time, or current.

Step 1: Determine the dimensions of momentum and the given quantities.✦ Active

The dimensions of momentum p=mv are [p]=[M][L][T]−1. The dimensions of the given quantities are:

[q]=[A][T] [I]=[A] [μ0]=[F][I]2=[M][L][T]−2[A]2=[M][L][T]−2[A]−2
Step 2: Calculate the dimensions for each option.○ Expand

Substitute the dimensions into each option:

Option 1: [qμ0/I]=([A][T])([M][L][T]−2[A]−2)[A]=[M][L][T]−1[A]−2 Option 2: [q2μ0I]=([A][T])2([M][L][T]−2[A]−2)[A]=[M][L][A] Option 3: [qI/μ0]=([A][T])([A])[M][L][T]−2[A]−2=[M]−1[L]−1[T]3[A]4 Option 4: [qμ0I]=([A][T])([M][L][T]−2[A]−2)([A])=[M][L][T]−1
Step 3: Compare with the dimensions of momentum.○ Expand

Comparing the calculated dimensions with the dimensions of momentum [M][L][T]−1, only Option 4, qμ0I, matches.

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