Four different pairs of physical quantities are given below. Pair having same dimensions will be?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Magnetisation and magnetic intensity
Compare the SI units of the quantities; quantities with the same unit have the same dimensions.
\( \text{Magnetic flux: } \mathrm{T\,m^{2}} \ (= \mathrm{Wb}) \)
\( \text{Magnetic moment: } \mathrm{A\,m^{2}} \)
\( \text{Magnetisation } M: \ \mathrm{A\,m^{-1}} \)
\( \text{Magnetic intensity } H: \ \mathrm{A\,m^{-1}} \)
\( \text{Magnetic field } B: \ \mathrm{T} \)
\( \text{Permeability } \mu: \ \mathrm{T\,m\,A^{-1}} \)
Magnetisation is magnetic moment per unit volume, \( \mathrm{A\,m^{2}/m^{3}} = \mathrm{A\,m^{-1}} \), the same unit as the magnetic intensity \( H \). Both have the dimensions \( [\mathrm{L^{-1}A}] \).
Option (1) Magnetic flux and magnetic moment — Incorrect. \( \mathrm{T\,m^{2}} \) and \( \mathrm{A\,m^{2}} \) are different units.
Option (2) Magnetisation and magnetic intensity — Correct. Both are measured in \( \mathrm{A\,m^{-1}} \).
Option (3) Magnetic field and magnetic permeability — Incorrect. \( \mathrm{T} \) and \( \mathrm{T\,m\,A^{-1}} \) differ by the factor \( \mathrm{m\,A^{-1}} \).
Option (4) Magnetisation and Magnetic field — Incorrect. \( M \) is in \( \mathrm{A\,m^{-1}} \), \( B \) in \( \mathrm{T} \); they are related by \( B = \mu_0(H + M) \), so they differ by the dimensions of \( \mu_0 \).
NCERT (2026-27):
Magnetisation and Magnetic Intensity – “… It is convenient to introduce another vector field H, called the magnetic intensity, which is defined by
\( \displaystyle \mathbf{H} = \frac{\mathbf{B}}{\mu_0} - \mathbf{M} \qquad (5.11) \)
where H has the same dimensions as M and is measured in units of A m−1.”