PhysicsCBSE Class 12 · Board exam 2023, set 55/1/1 · 3 marks · Short answer

CBSE Class 12 Physics 2023: question 26

Set in the CBSE Class 12 board exam of 2023, paper 55/1/1, section C, question 26, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26 · 3 marks · Short answerElectrostatic Potential and Capacitance

(a) Twelve negative charges of same magnitude are equally spaced and fixed on the circumference of a circle of radius R as shown in Fig. (i). Relative to potential being zero at infinity, find the electric potential and electric field at the centre C of the circle.

(b) If the charges are unequally spaced and fixed on an arc of $12 0^{\circ}$ of radius R as shown in Fig. (ii), find electric potential at the centre C.

Figure in the paper: Fig. (i): circle of radius R with 12 equally spaced charges on circumference, centre C. Fig. (ii): charges unequally spaced on an arc subtending $12 0^{\circ}$ at centre C, radius R. See it in the official paper.

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

Potential is a scalar — just add $k q / r$ for every charge.

Hint 2

For the field, pair each charge with the one diametrically opposite.

Hint 3

In (b), does the distance of any charge from C change?

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) Potential due to a point charge is $V = \frac{k q}{R}$ ; each of the 12 charges is $- q$ at distance R from C, and potential is a scalar, so $V = \frac{k ( - 12 q )}{R} = - \frac{12 q}{4 π ε _{0} R} = - \frac{3 q}{π ε _{0} R}$
1 mark
(a) Field: the charges are symmetrically placed, so field of each charge is cancelled by that of the diametrically opposite charge (equal magnitude, opposite direction). Hence $E = 0$ at C.
1 mark
(b) Potential is a scalar and depends only on the distance of each charge from C, not on their arrangement. All 12 charges are still at distance R, so $V = - \frac{12 q}{4 π ε _{0} R}$ (same as in (a)).
1 mark

Answer: (a) $V = - \frac{12 q}{4 π ε _{0} R}$ , $E = 0$ ; (b) $V = - \frac{12 q}{4 π ε _{0} R}$

Where the marks are

Potential at centre $- 12 q / (4 π ε_{0} R)$ (1 mark)
Electric field zero by symmetry (1 mark)
Same potential in (b), as potential is scalar, independent of arrangement (1 mark)

Revise the chapter

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

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

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CBSE Class 12 Physics 2023: question 26

Hints

Step-by-step solution

Revise the chapter

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