5.9. A circular coil of 16 turns and radius 10 cm carrying a current of 0.75 A rests with its plane normal to an external field of magnitude 5.0 \times 10 ^{-2} The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a frequency of 2.0 s^{-1} . What is the moment of inertia of the coil about its axis of rotation? 

Answers (1)

Given,

Number of turns, N = 16

Radius of the coil, r = 10 cm = 0.1 m

Current in the coil, I = 0.75 A

Magnetic field strength, B = 5.0 x 10^{-2} T

Frequency of oscillations of the coil, f = 2.0 s^{-1}

Now, Cross-section of the coil, A = \pi r^2 = \pi \times (0.1)^2 m^2

We know, Magnetic moment, m = NIA 

= (16)(0.75 A)(\pi \times (0.1)^2 m^2

= 0.377 JT^{-1}

We know, frequency of oscillation in a magnetic field is:

     f = \frac{1}{2\pi}\sqrt{\frac{MB}{I}}(I = Moment of Inertia of the coil)

 \implies I = \frac{MB}{4\pi^2f^2}

 \implies I = \frac{0.377\times5\times10^{-2}}{4\pi^22^2}

I = 1.19\times 10^{-4} kgm^2

The moment of inertia of the coil about its axis of rotation is 1.19 \times 10^{-4} kgm^2.

Most Viewed Questions

Related Chapters

Preparation Products

Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 39999/-
Buy Now
Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
Buy Now
NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
Buy Now
NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
NEET Foundation + Knockout NEET 2025 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions