Match List – I with List – II.
| LIST I | LIST II | ||
|---|---|---|---|
| A. | Cyclotron frequency | I. | \( \displaystyle\frac{NAB}{KR} \) |
| B. | Magnetic field due to a circular coil | II. | \( \displaystyle\frac{qB}{2\pi m} \) |
| C. | Magnetic field inside a toroid | III. | \( \displaystyle\frac{\mu_0 NI}{2\pi R} \) |
| D. | Voltage sensitivity | IV. | \( \displaystyle\frac{\mu_0 I}{2R} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A-II, B-IV, C-III, D-I
Each item has a standard formula, so each can be matched on its own.
(A) Cyclotron frequency — this matches (II) \( \frac{qB}{2\pi m} \). A particle of charge q and mass m moves in a circle in a field B with \( \omega = qB/m \), so its frequency is \( \nu = \omega/2\pi = qB/2\pi m \).
(B) Magnetic field due to a circular coil — this matches (IV) \( \frac{\mu_0 I}{2R} \). This is the field at the centre of a single circular loop of radius R carrying current I.
(C) Magnetic field inside a toroid — this matches (III) \( \frac{\mu_0 NI}{2\pi R} \). Ampere’s law over a circle of radius R inside the toroid with N turns gives \( B(2\pi R) = \mu_0NI \).
(D) Voltage sensitivity — this matches (I) \( \frac{NAB}{KR} \). The deflection of a galvanometer coil is \( \phi = NABI/K \), so the deflection per unit voltage, with \( I = V/R \), is \( \phi/V = NAB/KR \).
Note: Items (A), (B) and (D) of this question are from the latest textbook (2026-27). Item (C), the magnetic field inside a toroid, is printed only in the pre-rationalised textbook (2022-23). It was removed from the latest book, and it also appears to be out of the CUET 2026 syllabus.
NCERT (2026-27):
Summary – “… 3. In a uniform magnetic field B, a charge q executes a circular orbit in a plane normal to B. Its frequency of uniform circular motion is called the cyclotron frequency and is given by:
\( \displaystyle \nu_c = \frac{qB}{2\pi m} \)”
Magnetic Field on the Axis of a Circular Current Loop – “… As a special case of the above result, we may obtain the field at the centre of the loop. Here x = 0, and we obtain,
\( \displaystyle \mathbf{B}_0 = \frac{\mu_0 I}{2R}\,\hat{\mathbf{i}} \qquad (4.12) \)”
The Moving Coil Galvanometer – “… We define the voltage sensitivity as the deflection per unit voltage. From Eq. (4.26),
\( \displaystyle \frac{\phi}{V} = \left(\frac{NAB}{k}\right)\frac{I}{V} = \left(\frac{NAB}{k}\right)\frac{1}{R} \qquad (4.28) \)”
NCERT (Pre-rationalised edition, 2022-23):
The Toroid – “… The current enclosed Ie is (for N turns of toroidal coil) N I.
\( \displaystyle B\,(2\pi r) = \mu_0 N I, \qquad B = \frac{\mu_0 N I}{2\pi r} \qquad (4.21) \)”