### Electromagnetic Induction in a Rectangular Loop**Problem Statement:**A constant magnetic field passes through a single rectangular loop whose dimensions are \(0.33 \, \text{m} \times 0.44 \, \text{m}\). The magnetic field has a magnitude of \(1.9 \, \text{T}\) and is inclined at an angle of \(79^\circ\) with respect to the normal to the plane of the loop.**Questions:**1. **(a)** If the magnetic field decreases to zero in a time of \(0.49 \, \text{s}\), what is the magnitude of the average emf induced in the loop?2. **(b)** If the magnetic field remains constant at its initial value of \(1.9 \, \text{T}\), what is the magnitude of the rate \(\Delta A / \Delta t\) at which the area should change so that the average emf has the same magnitude?**Answer Inputs:**- **(a)** Number \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_) Units: [V]- **(b)** Number \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_) Units: [m\(^2\)/s]**Detailed Explanation:**To solve the given problems, we will use Faraday's law of electromagnetic induction and some basic trigonometry.### Details for Question (a):Faraday's law states that the induced emf (\(\mathcal{E}\)) in a loop is given by:\[\mathcal{E} = -\frac{d\Phi_B}{dt}\]where \(\Phi_B\) is the magnetic flux through the loop. The magnetic flux is defined as:\[\Phi_B = B \cdot A \cdot \cos(\theta)\]Here:- \(B\) is the magnitude of the magnetic field- \(A\) is the area of the rectangular loop- \(\theta\) is the angle between the magnetic field and the normal to the plane of the loopGiven that:- \(B = 1.9 \, \text{T}\)- \(\theta = 79^\circ\)- \(A = 0.33 \, \text{m} \times 0.44 \

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A constant magnetic field passes through a single rectangular loop whose dimensions are 0.33 m x 0.44 m. The magnetic field has a magnitude of 1.9 T and is inclined at an angle of 79° with respect to the normal to the plane of the loop. (a) If the magnetic field decreases to zero in a time of 0.49 s, what is the magnitude of the average emf induced in the loop? (b) If the magnetic field remains constant at its initial value of 1.9 T, what is the magnitude of the rate AA/At at which the area should change so that the average emf has the same magnitude? (a) Number i Units V V (b) Number i Units m^2/s

A constant magnetic field passes through a single rectangular loop whose dimensions are 0.33 m x 0.44 m. The magnetic field has a magnitude of 1.9 T and is inclined at an angle of 79° with respect to the normal to the plane of the loop. (a) If the magnetic field decreases to zero in a time of 0.49 s, what is the magnitude of the average emf induced in the loop? (b) If the magnetic field remains constant at its initial value of 1.9 T, what is the magnitude of the rate AA/At at which the area should change so that the average emf has the same magnitude? (a) Number i Units V V (b) Number i Units m^2/s

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter29: Magnetic Fields

Section: Chapter Questions

Problem 29.10OQ: A charged particle is traveling through a uniform magnetic field. Which of the following statements...

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