PhysicsCBSE Class 12 · Sample paper, session 2023-24 · 3 marks · Short answer

CBSE Class 12 Physics sample paper 2023-24: question 23

From the official CBSE sample question paper for 2023-24, section C, question 23, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 3 marks · Short answerElectrostatic Potential and Capacitance

Charges (+q) and (–q) are placed at the points A and B respectively which are a distance 2L apart. C is the midpoint between A and B. What is the work done in moving a charge +Q along the semicircle CRD.

Figure in the paper: Points A, C, B, D lie on a horizontal line in that order (A leftmost, D rightmost). A semicircle CRD is drawn above the line from C to D with top point R, with B at its centre (C and D on either side of B). See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Work done in moving a charge depends only on the potentials at the start and end points.

Hint 2

Find the distances of D from A and B: the semicircle has radius L with centre 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.

C is the midpoint of AB, so AC = BC = L. Potential at C:
$V_{C} = \frac{1}{4 π ε _{0}} (\frac{q}{L} - \frac{q}{L}) = 0$
1 mark
B is the centre of the semicircle of radius BC = L, so BD = L and AD = 3L. Potential at D:
$V_{D} = \frac{1}{4 π ε _{0}} (\frac{q}{3 L} - \frac{q}{L}) = - \frac{2 q}{3 ( 4 π ε _{0} ) L} = - \frac{q}{6 π ε _{0} L}$
1 mark
Work done does not depend on the path (electrostatic field is conservative):
$W = Q (V_{D} - V_{C}) = - \frac{Qq}{6 π ε _{0} L}$
1 mark

Answer: $W = - \frac{Qq}{6 π ε _{0} L}$

Where the marks are

$V_{C} = 0$ (1 mark)
$V_{D} = - q / (6 π ε_{0} L)$ (1 mark)
$W = Q (V_{D} - V_{C}) = - Qq / (6 π ε_{0} L)$ (1 mark)

Revise the chapter

Chapter: Electrostatic Potential and Capacitance (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Electrostatic Potential and Capacitance, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24: every question, by section.

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CBSE Class 12 Physics sample paper 2023-24: question 23

Hints

Step-by-step solution

Revise the chapter

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