Match List I with List II
| LIST I | LIST II |
| A. Gyromagnetic ratio | I. \( 4 \times 10^{-5}\,\mathrm{T} \) |
| B. Permeability of free space | II. \( 9.27 \times 10^{-24}\,\mathrm{A\,m^{2}} \) |
| C. Earth's magnetic field at equator | III. \( 8.8 \times 10^{10}\,\mathrm{C/kg} \) |
| D. Bohr magneton | IV. \( 12.56 \times 10^{-7}\,\mathrm{T\,m\,A^{-1}} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A-III, B-IV, C-I, D-II
The four quantities are told apart by their units first, and then by their values.
(A) Gyromagnetic ratio — this matches (III) \( 8.8 \times 10^{10}\,\mathrm{C/kg} \). It is the ratio of the magnetic moment to the angular momentum of an orbiting electron, which works out to \( e/2m_e \), a charge per unit mass.
\( \displaystyle \frac{e}{2m_e} = \frac{1.6\times10^{-19}\,\mathrm{C}}{2 \times 9.1\times10^{-31}\,\mathrm{kg}} \approx 8.8\times10^{10}\,\mathrm{C/kg} \)
(B) Permeability of free space — this matches (IV) \( 12.56 \times 10^{-7}\,\mathrm{T\,m\,A^{-1}} \). Its value is \( \mu_0 = 4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}} \), and \( 4\pi \approx 12.56 \); no other quantity in List I has this unit.
(C) Earth's magnetic field at equator — this matches (I) \( 4 \times 10^{-5}\,\mathrm{T} \). A magnetic field is measured in tesla, and the earth's field at its surface is of the order of \( 10^{-5}\,\mathrm{T} \), about \( 4\times10^{-5}\,\mathrm{T} \).
(D) Bohr magneton — this matches (II) \( 9.27 \times 10^{-24}\,\mathrm{A\,m^{2}} \). It is the magnetic moment of an electron in the first Bohr orbit, so its unit is that of a magnetic moment, A m\( ^{2} \).
\( \displaystyle \mu_B = \frac{e h}{4\pi m_e} = \frac{1.6\times10^{-19} \times 6.63\times10^{-34}}{4\pi \times 9.1\times10^{-31}} \approx 9.27\times10^{-24}\,\mathrm{A\,m^{2}} \)
Note: Items (B) and (C) of this question are from the latest textbook (2026-27). Items (A) and (D), the gyromagnetic ratio and the Bohr magneton, are printed only in the pre-rationalised textbook (2022-23). They were removed from the latest book, and they also appear to be out of the CUET 2026 syllabus.
NCERT (2026-27):
Magnetic Field Due to a Current Element, Biot-Savart Law – “… The proportionality constant in SI units has the exact value,
\( \displaystyle \frac{\mu_0}{4\pi} = 10^{-7}\ \mathrm{T\,m/A} \qquad [4.7(c)] \)
We call μ0 the permeability of free space (or vacuum).”
Magnetic Force on a Current-Carrying Conductor – “… The earth’s magnetic field is approximately 4 × 10–5 T and we have ignored it.”
NCERT (Pre-rationalised edition, 2022-23):
The Magnetic Dipole Moment of a Revolving Electron – “… The ratio
\( \displaystyle \frac{\mu_l}{l} = \frac{e}{2m_e} \qquad (4.35) \)
is called the gyromagnetic ratio and is a constant. Its value is 8.8 × 1010 C /kg for an electron, which has been verified by experiments.”
The Magnetic Dipole Moment of a Revolving Electron – “… Take the value n = 1, we have from Eq. (4.34) that,
\( \displaystyle (\mu_l)_{\min} = \frac{e h}{4\pi m_e} = 9.27 \times 10^{-24}\ \mathrm{A\,m^2} \qquad (4.37) \)
where the subscript ‘min’ stands for minimum. This value is called the Bohr magneton.”