PhysicsCBSE Class 12 · Board exam 2025, set 55/7/1 · 5 marks · Long answer

CBSE Class 12 Physics 2025: question 32(b)

Set in the CBSE Class 12 board exam of 2025, paper 55/7/1, section E, question 32(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(b) · 5 marks · Long answerMoving Charges and Magnetism

(i) (I) Write Ampere's circuital law in mathematical form and explain the terms used.
(II) As the current carrying solenoid is made longer, the magnetic field produced outside it approaches zero. Why ?
(III) A flexible loop of irregular shape carrying current when located in an external magnetic field, changes to a circular shape. Give reason.
(ii) A galvanometer of resistance G is converted into a voltmeter to measure up to V volts, by connecting a resistance $R_{1}$ in series with the coil. If $R_{1}$ is replaced by $R_{2}$ , then it can only measure up to $\frac{V}{2}$ volt. Find the value of the resistance $R_{3}$ (in terms of $R_{1}$ and $R_{2}$ ) needed to convert it into a voltmeter that can read up to 2 V.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 55/7/1.

Hints

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

Hint 1

For a voltmeter, the full-scale current $I_{g}$ flows through $G$ and the series resistance together, so $V = I_{g} (G + R)$ .

Hint 2

Write this relation for ranges $V$ and $V /2$ , then eliminate $V / I_{g}$ to find $G$ in terms of $R_{1}$ and $R_{2}$ .

Hint 3

For range $2 V$ , use $R_{3} = 2 V / I_{g} - G$ .

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)(I) Ampere's circuital law: $\oint B \cdot d l = μ_{0} I_{e}$ . Here $B$ is the magnetic field at the small element $d l$ of a closed (Amperian) loop, $d l$ is a small length element along the loop, $I_{e}$ is the net current enclosed by (passing through the surface bounded by) the loop, and $μ_{0}$ is the permeability of free space.
1 mark
(II) As the solenoid is made longer, its closely wound turns behave like a long continuous cylindrical current sheet. The field lines spread out over a very large region outside, so the field density outside becomes negligible. Hence the field outside approaches zero, while the field inside stays uniform and strong.
1 mark
(III) In a uniform magnetic field, a current loop experiences forces that make it spread out so that the magnetic flux through it (and its magnetic moment $m = I A$ ) becomes maximum. For a given perimeter, a circle encloses the greatest area of any shape. So the flexible loop takes a circular shape, which gives maximum area and maximum flux.
1 mark
(ii) Let $I_{g}$ be the full-scale current of the galvanometer. For a voltmeter of range $V$ : $V = I_{g} (G + R)$ .
With $R_{1}$ : $\frac{V}{I _{g}} = R_{1} + G$ ...(1)
With $R_{2}$ (range $V /2$ ): $\frac{V}{2 I _{g}} = R_{2} + G$ ...(2)
Putting (1) in (2): $R_{1} + G = 2 (R_{2} + G)$ , so $G = R_{1} - 2 R_{2}$ .
1 mark
For range $2 V$ : $R_{3} = \frac{2 V}{I _{g}} - G = 2 (R_{1} + G) - G = 2 R_{1} + G$ .
Substituting $G$ : $R_{3} = 2 R_{1} + R_{1} - 2 R_{2} = 3 R_{1} - 2 R_{2}$ .
1 mark

Answer: (i)(I) $\oint B \cdot d l = μ_{0} I_{e}$ ; (II) a long solenoid acts like a cylindrical current sheet, so the outside field tends to zero; (III) a circle encloses maximum area, so the flux is maximum; (ii) $R_{3} = 3 R_{1} - 2 R_{2}$

Where the marks are

States $\oint B \cdot d l = μ_{0} I_{e}$ and explains $B$ , $d l$ and $I_{e}$ (1 mark)
Reason: a long solenoid behaves like a cylindrical current sheet, so the outside field approaches zero (1 mark)
Reason: a circle has maximum area for a given perimeter, so the flux through the loop is maximum (1 mark)
Writes $V / I_{g} = R_{1} + G$ and $V /2 I_{g} = R_{2} + G$ and obtains $G = R_{1} - 2 R_{2}$ (1 mark)
Obtains $R_{3} = 3 R_{1} - 2 R_{2}$ (1 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 paper2025 board paper, set 55/7/1: every question, by section.

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CBSE Class 12 Physics 2025: question 32(b)

Hints

Step-by-step solution

Revise the chapter

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