PhysicsCBSE Class 12 · Board exam 2023, set 55/1/1 · 2 marks · Very short answer

CBSE Class 12 Physics 2023: question 19

Set in the CBSE Class 12 board exam of 2023, paper 55/1/1, 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

An alpha particle is projected with velocity $v = (3 \cdot 0 \times 1 0^{5} m/s) \hat{i}$ into a region in which magnetic field $B = [(0 \cdot 4 T) \hat{i} + (0 \cdot 3 T) \hat{j}]$ exists. Calculate the acceleration of the particle in the region. $\hat{i}$ , $\hat{j}$ and $\hat{k}$ are unit vectors along x, y and z axis respectively and charge to mass ratio for alpha particle is $4 \cdot 8 \times 1 0^{7}$ C/kg.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 55/1/1.

Hints

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

Hint 1

The force on a charge moving in a magnetic field is the Lorentz magnetic force $q (v \times B)$ .

Hint 2

Only the component of $B$ perpendicular to $v$ contributes; $\hat{i} \times \hat{i} = 0$ .

Hint 3

Divide force by mass using the given charge-to-mass ratio; keep the unit vector.

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.

Force on a moving charge: $F = q (v \times B) = q [(3.0 \times 1 0^{5}) \hat{i} \times (0.4 \hat{i} + 0.3 \hat{j})]$
½ mark
Using $\hat{i} \times \hat{i} = 0$ and $\hat{i} \times \hat{j} = \hat{k}$ : $F = q (0.9 \times 1 0^{5}) \hat{k}$ N
½ mark
By Newton's second law, $a = \frac{F}{m} = \frac{q}{m} (0.9 \times 1 0^{5}) \hat{k}$
½ mark
$a = 4.8 \times 1 0^{7} \times 0.9 \times 1 0^{5} \hat{k} = 4.32 \times 1 0^{12} \hat{k} m s^{- 2}$ , i.e. along the +z axis.
½ mark

Answer: $a = 4.32 \times 1 0^{12} \hat{k}$ m s $^{- 2}$ (along +z axis)

Where the marks are

Writes $F = q (v \times B)$ with values substituted (½ mark)
Evaluates cross product to get $q (0.9 \times 1 0^{5}) \hat{k}$ (½ mark)
Uses $a = F / m = (q / m) (0.9 \times 1 0^{5}) \hat{k}$ (½ mark)
Final $4.32 \times 1 0^{12} \hat{k}$ m s $^{- 2}$ with direction (½ mark; ½ deducted if direction missing)

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 paper2023 board paper, set 55/1/1: every question, by section.

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CBSE Class 12 Physics 2023: question 19

Hints

Step-by-step solution

Revise the chapter

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