A circular coil of radius 8·0 cm and 40 turns is rotated about its vertical diameter with an angular speed of (25)/(π) rad s^-1 in a uniform horizontal magnetic field of magnitude 3·0×10^-2 T. The maximum emf induced in the coil is : (A) 0·12 V (B) 0·15 V (C) 0·19 V (D) 0·22 V

PhysicsCBSE Class 12 · Board exam 2023, set 55/1/1 · 1 mark · MCQ

CBSE Class 12 Physics 2023: question 6

Set in the CBSE Class 12 board exam of 2023, paper 55/1/1, section A, question 6, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q6 · 1 mark · MCQElectromagnetic Induction

A circular coil of radius $8 \cdot 0$ cm and 40 turns is rotated about its vertical diameter with an angular speed of $\frac{25}{π}$ rad s $^{- 1}$ in a uniform horizontal magnetic field of magnitude $3 \cdot 0 \times 1 0^{- 2}$ T. The maximum emf induced in the coil is :

(A)0·12 V
(B)0·15 V
(C)0·19 V
(D)0·22 V

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

Recall the peak emf of a rotating coil.

Hint 2

$e_{0} = N B A ω$ , with $A = π r^{2}$ ; notice that the $π$ cancels.

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.

The maximum emf is $e_{0} = N B A ω = 40 \times 3 \times 1 0^{- 2} \times π (0.08)^{2} \times \frac{25}{π}$ .
½ mark
$e_{0} = 40 \times 0.03 \times 0.0064 \times 25 = 0.192 \approx 0.19$ V. This is option (C).
½ mark

Answer: 0.19 V, option (C)

Where the marks are

Uses $e_{0} = N B A ω$ and gets 0.19 V (1 mark)

Revise the chapter

Chapter: Electromagnetic Induction (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Electromagnetic Induction, 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 6

Hints

Step-by-step solution

Revise the chapter

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