PhysicsCBSE Class 12 · Sample paper, session 2024-25 · 2 marks · Very short answer

CBSE Class 12 Physics sample paper 2024-25: question 19

From the official CBSE sample question paper for 2024-25, section B, question 19, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q19 · 2 marks · Very short answerMoving Charges and Magnetism

P and Q are two identical charged particles each of mass $4 \times 1 0^{- 26}$ kg and charge $4.8 \times 1 0^{- 19}$ C, each moving with the same speed of $2.4 \times 1 0^{5}$ m/s as shown in the figure. The two particles are equidistant (0.5 m) from the vertical Y-axis. At some instant, a magnetic field B is switched on so that the two particles undergo head-on collision.

Find –
(I) the direction of the magnetic field and
(II) the magnitude of the magnetic field applied in the region.

Figure in the paper: X-Y axes. Particle P (positive) at upper left of a 1 m vertical marker, 1 m above the X-axis on the right side of Y-axis, moving left (toward Y-axis). Particle Q (positive) on the X-axis left of the Y-axis, moving right. Each is 0.5 m from the Y-axis; vertical separation 1 m. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

For the particles to meet head-on, P must bend down and Q must bend up; use $F = q v \times B$ to find B.

Hint 2

Where do the two curved paths meet? That fixes the radius of each path.

Hint 3

Then apply $r = m v / q B$ .

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) Set up axes: +x to the right, +y up, +z out of the page. P (upper, moving in −x) must curve downward and Q (lower, moving in +x) must curve upward, so that they meet head-on on the Y-axis.
For P: $F = q (v \times B)$ must point along $- \overset{y}{^}$ . Since $(- \hat{i}) \times (- \hat{k}) = - \hat{j}$ , B must be along $- \hat{k}$ . Check for Q: $\hat{i} \times (- \hat{k}) = + \hat{j}$ , upward, as required. So the field is perpendicular to the plane of the paper, directed inwards.
½ mark
(II) Each particle travels a quarter circle and both reach the point (0, 0.5 m) at the same instant, moving in opposite directions. This requires a radius equal to the distance from the Y-axis: $r = 0.5$ m.
½ mark
$r = \frac{m v}{q B} \Rightarrow B = \frac{m v}{q r}$
½ mark
$B = \frac{4 \times 1 0 ^{- 26} \times 2.4 \times 1 0 ^{5}}{4.8 \times 1 0 ^{- 19} \times 0.5} = \frac{9.6 \times 1 0 ^{- 21}}{2.4 \times 1 0 ^{- 19}} = 0.04 T$
½ mark

Answer: (I) B perpendicular to the plane of the paper, into it; (II) B = 0.04 T

Where the marks are

Correct direction of B: into the plane of the paper (½ mark)
Recognises that the radius must be 0.5 m (½ mark)
Uses $r = m v / q B$ (½ mark)
Gets B = 0.04 T (½ 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 paperSample paper 2024-25: every question, by section.

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CBSE Class 12 Physics sample paper 2024-25: question 19

Hints

Step-by-step solution

Revise the chapter

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