At what speed (in meters per second) must the sliding rod in the figure below move to produce an emf of 1.00 V in a 1.35 T field directed perpendicular to the rods and into the page, given the rod's length is 32.5 cm? ____ m/s
At what speed (in meters per second) must the sliding rod in the figure below move to produce an emf of 1.00 V in a 1.35 T field directed perpendicular to the rods and into the page, given the rod's length is 32.5 cm? ____ m/s
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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At what speed (in meters per second) must the sliding rod in the figure below move to produce an emf of 1.00 V in a 1.35 T field directed perpendicular to the rods and into the page, given the rod's length is 32.5 cm?
____ m/s
![### Determining the Speed of a Sliding Rod to Produce Electromotive Force
**Problem:**
At what speed (in meters per second) must the sliding rod in the figure move to produce an emf of 1.00 V in a 1.35 T field directed perpendicular to the rods and into the page, given the rod's length is 32.5 cm?
#### Explanation of Diagrams
**Diagram 1:**
- The diagram illustrates a sliding rod moving to the right with velocity \( v \).
- The rod is within a magnetic field (\( B_{\text{in}} \)) represented by the crosses, indicating the field direction is into the page.
- The area change \(\Delta A = \ell \Delta x\) occurs as the rod moves.
- The change in magnetic flux over time (\(\Delta x / \Delta t\)) contributes to the generation of emf.
**Diagram 2:**
- Displays the application of Lenz's Law.
- As the rod moves, it creates an increasing magnetic flux (\(\Phi\)) within a closed loop.
- The resistance (\( R \)) and induced current (\( I \)) are shown, driven by the generated emf.
- Right-Hand Rule (RHR-1) shows the direction of induced force (\( F \)), magnetic field (\( B \)), and velocity (\( v \)).
**Key Concepts:**
- **Faraday’s Law:** The emf (\( \epsilon \)) is induced by the change in magnetic flux, expressed as \( \epsilon = B\ell v \).
- **Lenz's Law:** Describes the direction of the induced current generated in the loop, opposing the change in flux.
- **Right-Hand Rule:** Used to determine the direction of the force and current relative to the magnetic field and velocity.
**Given Values:**
- Emf (\( \epsilon \)) = 1.00 V
- Magnetic Field (\( B \)) = 1.35 T
- Rod length (\( \ell \)) = 32.5 cm = 0.325 m
**Calculation:**
To find \( v \):
\[ \epsilon = B\ell v \]
\[ v = \frac{\epsilon}{B\ell} \]
\[ v = \frac{1.00 \, \text{V}}{1.35 \, \text{T} \times 0.325](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F238fed3b-2fcf-40ca-a8e1-295985b4dcab%2Fce5ffe08-5c56-47df-920a-ecb9f2e17c8e%2Fbypt8li_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining the Speed of a Sliding Rod to Produce Electromotive Force
**Problem:**
At what speed (in meters per second) must the sliding rod in the figure move to produce an emf of 1.00 V in a 1.35 T field directed perpendicular to the rods and into the page, given the rod's length is 32.5 cm?
#### Explanation of Diagrams
**Diagram 1:**
- The diagram illustrates a sliding rod moving to the right with velocity \( v \).
- The rod is within a magnetic field (\( B_{\text{in}} \)) represented by the crosses, indicating the field direction is into the page.
- The area change \(\Delta A = \ell \Delta x\) occurs as the rod moves.
- The change in magnetic flux over time (\(\Delta x / \Delta t\)) contributes to the generation of emf.
**Diagram 2:**
- Displays the application of Lenz's Law.
- As the rod moves, it creates an increasing magnetic flux (\(\Phi\)) within a closed loop.
- The resistance (\( R \)) and induced current (\( I \)) are shown, driven by the generated emf.
- Right-Hand Rule (RHR-1) shows the direction of induced force (\( F \)), magnetic field (\( B \)), and velocity (\( v \)).
**Key Concepts:**
- **Faraday’s Law:** The emf (\( \epsilon \)) is induced by the change in magnetic flux, expressed as \( \epsilon = B\ell v \).
- **Lenz's Law:** Describes the direction of the induced current generated in the loop, opposing the change in flux.
- **Right-Hand Rule:** Used to determine the direction of the force and current relative to the magnetic field and velocity.
**Given Values:**
- Emf (\( \epsilon \)) = 1.00 V
- Magnetic Field (\( B \)) = 1.35 T
- Rod length (\( \ell \)) = 32.5 cm = 0.325 m
**Calculation:**
To find \( v \):
\[ \epsilon = B\ell v \]
\[ v = \frac{\epsilon}{B\ell} \]
\[ v = \frac{1.00 \, \text{V}}{1.35 \, \text{T} \times 0.325
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