**Problem Statement:**The 12.0 cm long rod in Figure 23.11 (a) moves at 4.00 m/s. What is the strength of the magnetic field if a 95.0 V emf is induced?**Diagrams Explanation:****Figure 23.11 (a):**- A rectangular loop is shown with a rod moving perpendicularly along the top of the loop. - The loop is situated within a uniform magnetic field (indicated by 'x'), pointing into the page.- The motion of the rod is represented by the velocity \( v \), moving towards the right. - The area of the loop changes as \( \Delta A = l \times \Delta x \).- The rod moves by a distance \( \Delta x \) in a time interval \( \Delta t \).**Figure 23.11 (b):**- Shows two views explaining the application of Lenz's Law and the use of Right-Hand Rule (RHR).- The top part of the diagram uses RHR-2 to indicate the direction of the induced current within the loop due to the moving rod.- Beneath the loop, an equivalent circuit is depicted with a resistor \( R \) and an electromotive force \( \mathcal{E} \).- The magnetic flux \( \Phi \) is shown to be increasing.**Important Concepts Illustrated:**- Right-Hand Rule (RHR) is used to determine the direction of the magnetic force and induced current.- Lenz’s Law is applied to determine the direction of the induced current as one that opposes the change in magnetic flux.- The induced emf (\( \mathcal{E} \)) is related to the rate of change of the magnetic flux, demonstrating Faraday's law of electromagnetic induction.This set-up helps in understanding the principles behind electromagnetic induction and the factors affecting the magnitude of induced emf in a closed circuit.

For the given situation Length of rod (l) = 12.0 cm = 0.12 m Velocity of rod v = 4 m/s Emf induced…

Answered: 16. The 12.0 cm long rod in Figure…

16. The 12.0 cm long rod in Figure 23.11 (a) moves at 4.00 m/s. What is the strength of the magnetic field if a 95.0 V emf is induced? ΔΑ-Δx B At (a)

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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Concept explainers

Electromagnets

The word "electromagnet" is composed of two words, ‘electro’ and ‘magnet’. It is a type of magnet in which an electric current helps in the generation of a magnetic field. Electromagnets usually consist of two major parts, wire and a coil around which the wire is wound. This is called a solenoid. When an electric current is allowed to pass through the coiled wire, the electric current produces a magnetic field. This magnetic field is present only when current is passing through the wire.

Question

**Problem Statement:**
The 12.0 cm long rod in Figure 23.11 (a) moves at 4.00 m/s. What is the strength of the magnetic field if a 95.0 V emf is induced?

**Diagrams Explanation:**

**Figure 23.11 (a):**
- A rectangular loop is shown with a rod moving perpendicularly along the top of the loop.
- The loop is situated within a uniform magnetic field (indicated by 'x'), pointing into the page.
- The motion of the rod is represented by the velocity \( v \), moving towards the right.
- The area of the loop changes as \( \Delta A = l \times \Delta x \).
- The rod moves by a distance \( \Delta x \) in a time interval \( \Delta t \).

**Figure 23.11 (b):**
- Shows two views explaining the application of Lenz's Law and the use of Right-Hand Rule (RHR).
- The top part of the diagram uses RHR-2 to indicate the direction of the induced current within the loop due to the moving rod.
- Beneath the loop, an equivalent circuit is depicted with a resistor \( R \) and an electromotive force \( \mathcal{E} \).
- The magnetic flux \( \Phi \) is shown to be increasing.

**Important Concepts Illustrated:**
- Right-Hand Rule (RHR) is used to determine the direction of the magnetic force and induced current.
- Lenz’s Law is applied to determine the direction of the induced current as one that opposes the change in magnetic flux.
- The induced emf (\( \mathcal{E} \)) is related to the rate of change of the magnetic flux, demonstrating Faraday's law of electromagnetic induction.

This set-up helps in understanding the principles behind electromagnetic induction and the factors affecting the magnitude of induced emf in a closed circuit.

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