**Question 12:** You place a wire hoop with a diameter of 2.5 cm inside a region of space with a changing magnetic field and measure a voltage of -5 V. What is the rate of change of the magnetic field, and is it increasing or decreasing?### Explanation:This question involves understanding electromagnetic induction. Given the setup with a wire hoop and a changing magnetic field, you can use Faraday's law of electromagnetic induction to determine the rate of change of the magnetic field:\[ \text{Voltage} = - \dfrac{d\Phi}{dt} \]where \( \Phi \) is the magnetic flux through the hoop. The negative sign indicates the direction of induced voltage as per Lenz's law.To find the rate of change of the magnetic field (\( \dfrac{dB}{dt} \)), you need to calculate the area of the hoop and then solve for \( \dfrac{dB}{dt} \) using the measured voltage.**Calculation Details:**1. **Area of the Hoop:** The diameter of the hoop is given as 2.5 cm, so the radius \( r = 1.25 \) cm = 0.0125 m. \[ \text{Area} = \pi r^2 = \pi (0.0125)^2 \, \text{m}^2 \]2. **Magnetic Flux (\( \Phi \)):** \[ \Phi = B \times \text{Area} \]3. **Using Faraday’s Law:** \[ -5 \, \text{V} = - \dfrac{d(B \cdot \text{Area})}{dt} \] \[ 5 = \text{Area} \times \dfrac{dB}{dt} \]4. **Solve for \( \dfrac{dB}{dt} \):** \[ \dfrac{dB}{dt} = \frac{5}{\text{Area}} \]By calculating the area, you can find the numerical value of \( \dfrac{dB}{dt} \). The negative voltage signifies that the magnetic field is increasing in the direction opposite to the assumed positive directional flux.

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[Q12] You place a wire hoop with a diameter of 2.5 cm inside a region of space with a changing magnetic field, and measure a voltage of -5 V. What is the rate of change of the magnetic field, and is it increasing or decreasing?

[Q12] You place a wire hoop with a diameter of 2.5 cm inside a region of space with a changing magnetic field, and measure a voltage of -5 V. What is the rate of change of the magnetic field, and is it increasing or decreasing?

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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