**Problem 1: Induced EMF in a Shrinking Circular Loop**A certain elastic conducting material is stretched into a circular loop of 12.0 cm radius. It is placed with its plane perpendicular to a uniform 0.800 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 75.0 cm/s. What emf is induced in the loop at that instant? (See problem 2, chapter 30 in Fundamentals of Physics)*Explanation:*To find the induced emf (electromotive force) in the loop, we can use Faraday's Law of Induction. According to Faraday's Law, the induced emf is given by:\[ \mathcal{E} = - \frac{d\Phi_B}{dt} \]where \( \Phi_B \) is the magnetic flux through the loop. \( \Phi_B \) is given by:\[ \Phi_B = B \cdot A \]Here:- \( B \) is the magnetic field strength (0.800 T).- \( A \) is the area of the loop. For a circle, \( A = \pi r^2 \), where \( r \) is the radius.Since the radius \( r \) is changing with time, we need to account for its rate of change (\( \frac{dr}{dt} \)). Therefore:\[ A = \pi r^2 \]The rate of change of area with respect to time \( \frac{dA}{dt} \) can be found using the chain rule:\[ \frac{dA}{dt} = \frac{d}{dt} (\pi r^2) = 2\pi r \frac{dr}{dt} \]Given:- \( r = 12.0 \) cm = 0.120 m- \( \frac{dr}{dt} = -75.0 \) cm/s = -0.750 m/s (the negative sign indicates that the radius is shrinking)Then:\[ \frac{dA}{dt} = 2\pi (0.120 \, \text{m})(-0.750 \, \text{m/s}) \]\[ \frac{dA}{dt} = -0.180 \pi \, \text{m}^2/\text{s} \]Finally, the induced emf

according to faraday law whenever there is a change in flux passing through any closed loop their is…

1. A certain elastic conducting material is stretched into a circular loop of 12.0 cm radius. It is placed with its plane perpendicular to a uniform 0.800 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 75.0 cm/s. What emf is induced in the loop at that instant? (See problem 2, chapter 30 in Fundamentals of Physics)

1. A certain elastic conducting material is stretched into a circular loop of 12.0 cm radius. It is placed with its plane perpendicular to a uniform 0.800 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 75.0 cm/s. What emf is induced in the loop at that instant? (See problem 2, chapter 30 in Fundamentals of Physics)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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