PhysicsCBSE Class 12 · Board exam 2025, set 55/1/1 · 5 marks · Long answer

CBSE Class 12 Physics 2025: question 32(a)

Set in the CBSE Class 12 board exam of 2025, paper 55/1/1, section E, question 32(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(a) · 5 marks · Long answerMoving Charges and Magnetism

(i) A proton moving with velocity $V$ in a non-uniform magnetic field traces a path as shown in the figure.
The path followed by the proton is always in the plane of the paper. What is the direction of the magnetic field in the region near points P, Q and R ? What can you say about relative magnitude of magnetic fields at these points ?
(ii) A current carrying circular loop of area A produces a magnetic field B at its centre. Show that the magnetic moment of the loop is $\frac{2 B A}{μ _{0}} \frac{A}{π}$ .

Figure in the paper: A proton (+) with velocity V moves horizontally to the right to point P, then the path curves upward through Q to R, bending upward, then curving over at the top near R; the path lies in the plane of the paper. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 55/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

The force on the proton points towards the inside of each bend. Use $F = q v \times B$ to find which way B must point.

Hint 2

The speed does not change in a magnetic field, so a tighter bend means a stronger field ( $r = m v / q B$ ). For (ii), express I and r in terms of B and A.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(i) The force on the proton is $F = q (v \times B)$ and points towards the centre of curvature of the path. Near P the path bends upward (force upward) while v is to the right, so B is into the plane of the paper.
½ mark
Near Q the path still bends upward (force towards the upper side), so B is again into the plane of the paper.
½ mark
Near R the path bends the other way (force downward), so B is out of the plane of the paper.
½ mark
The magnetic force does no work, so the speed is constant. Radius of curvature $r = \frac{m v}{q B}$ , so $B \propto \frac{1}{r}$ .
½ mark
Near Q the path is least curved (largest radius), so B is smallest there. Near P the curvature is moderate. Near R the path is most sharply curved (smallest radius), so B is largest.
½ mark
Hence $B_{Q} < B_{P} < B_{R}$ .
½ mark
(ii) The field at the centre of the loop is $B = \frac{μ _{0} I}{2 r}$ , so $I = \frac{2 B r}{μ _{0}}$ . Area $A = π r^{2}$ , so $r = \frac{A}{π}$ .
1 mark
Magnetic moment $m = I A = \frac{2 B r}{μ _{0}} A = \frac{2 B A}{μ _{0}} \frac{A}{π}$ . Hence shown.
1 mark

Answer: (i) B into the page near P and Q, out of the page near R; B_Q < B_P < B_R. (ii) m = (2BA/μ₀)√(A/π)

Where the marks are

Direction of B near P, Q and R using $F = q v \times B$ (½ + ½ + ½ mark)
Uses $r = m v / q B$ to compare magnitudes and concludes $B_{Q} < B_{P} < B_{R}$ (½ + ½ + ½ mark)
Writes $I = 2 B r / μ_{0}$ and $r = A / π$ (1 mark)
Gets $m = I A = \frac{2 B A}{μ _{0}} A / π$ (1 mark)

Revise the chapter

Chapter: Moving Charges and Magnetism (notes, formulas, where marks are lost and every past question)
Topic: Motion of a Charge in a Magnetic Field

Practise this chapterBoard-style questions from Moving Charges and Magnetism, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 55/1/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 12 Physics 2025: question 32(a)

Hints

Step-by-step solution

Revise the chapter

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