PhysicsCBSE Class 12 · Board exam 2024, set 55/1/1 · 3 marks · Short answer

CBSE Class 12 Physics 2024: question 24

Set in the CBSE Class 12 board exam of 2024, paper 55/1/1, section C, question 24, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 3 marks · Short answerMoving Charges and Magnetism

A proton with kinetic energy $1.3384 \times 1 0^{- 14}$ J moving horizontally from north to south, enters a uniform magnetic field B of 2.0 mT directed eastward. Calculate :
(a) the speed of the proton
(b) the magnitude of acceleration of the proton
(c) the radius of the path traced by the proton
[Take (q/m) for proton = $1.0 \times 1 0^{8}$ C/kg]

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 55/1/1.

Hints

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

Hint 1

Get the speed from the kinetic energy and the proton's mass.

Hint 2

The velocity is perpendicular to B, so the force is qvB. Divide by m using the given q/m.

Hint 3

Equate qvB to the centripetal force $m v^{2} / r$ .

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.

(a) From $K = \frac{1}{2} m v^{2}$ : $v = \frac{2 K}{m}$ .
½ mark
With $m = 1.673 \times 1 0^{- 27}$ kg: $v = \frac{2 \times 1.3384 \times 1 0 ^{- 14}}{1.673 \times 1 0 ^{- 27}} = 1.6 \times 1 0^{13} = 4 \times 1 0^{6}$ m/s.
½ mark
(b) $v$ (southward) is perpendicular to $B$ (eastward), so the magnetic force is $F = q v B$ and $a = \frac{q v B}{m} = (\frac{q}{m}) v B$ .
½ mark
$a = 1.0 \times 1 0^{8} \times 4 \times 1 0^{6} \times 2.0 \times 1 0^{- 3} = 8 \times 1 0^{11} m/s^{2}$
½ mark
(c) The magnetic force supplies the centripetal force, $q v B = \frac{m v ^{2}}{r}$ , so $r = \frac{m v}{q B} = \frac{v}{( q / m ) B}$ .
½ mark
$r = \frac{4 \times 1 0 ^{6}}{1.0 \times 1 0 ^{8} \times 2.0 \times 1 0 ^{- 3}} = 20$ m
½ mark

Answer: (a) 4 × 10⁶ m/s; (b) 8 × 10¹¹ m/s²; (c) 20 m

Where the marks are

Formula for speed from kinetic energy (½ mark)
v = 4 × 10⁶ m/s (½ mark)
Uses $a = q v B / m$ (½ mark)
a = 8 × 10¹¹ m/s² (½ mark)
Uses $r = m v / q B$ (½ mark)
r = 20 m (½ mark)

Revise the chapter

Chapter: Moving Charges and Magnetism (notes, formulas, where marks are lost and every past question)

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 paper2024 board paper, set 55/1/1: every question, by section.

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CBSE Class 12 Physics 2024: question 24

Hints

Step-by-step solution

Revise the chapter

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