A metal rod with a length of 27.0 cm lies in the ry-plane and makes an angle of 39.0° with the positive z-axis and an angle of 51.0° with the positive y-axis. The rod is moving in the +z-direction with a speed of 6.80 m/s. The rod is in a uniform magnetic field B = (0.200 T)i – (0.280 T)j – (0.0900 T)k. Part A What is the magnitude of the emf induced in the rod? Express your answer in volts. ? E = V Submit Request Answer
A metal rod with a length of 27.0 cm lies in the ry-plane and makes an angle of 39.0° with the positive z-axis and an angle of 51.0° with the positive y-axis. The rod is moving in the +z-direction with a speed of 6.80 m/s. The rod is in a uniform magnetic field B = (0.200 T)i – (0.280 T)j – (0.0900 T)k. Part A What is the magnitude of the emf induced in the rod? Express your answer in volts. ? E = V Submit Request Answer
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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![### Problem Statement:
A metal rod with a length of 27.0 cm lies in the xy-plane and makes an angle of 39.0° with the positive x-axis and an angle of 51.0° with the positive y-axis. The rod is moving in the +x-direction with a speed of 6.80 m/s. The rod is in a uniform magnetic field:
\[ \mathbf{B} = (0.200 \ \text{T}) \hat{i} - (0.280 \ \text{T}) \hat{j} - (0.0900 \ \text{T}) \hat{k} \]
### Part A:
**Question:**
What is the magnitude of the emf induced in the rod?
**Requirement:**
Express your answer in volts.
**Field:**
Electricity & Magnetism
**Equation to use:**
The electromotive force (emf) induced in the rod moving through a magnetic field is given by Faraday's Law of Induction, specifically for a moving conductor:
\[ \mathcal{E} = \mathbf{v} \times \mathbf{B} \cdot \mathbf{l} \]
where:
- \(\mathbf{v}\) is the velocity of the rod,
- \(\mathbf{B}\) is the magnetic field,
- \(\mathbf{l}\) is the length vector of the rod.
### Input Box
```
\mathcal{E} =
[TextInput: 0.00] V
```
**Buttons:**
- Submit
- Request Answer
### Instructions to Students:
To solve this problem:
1. Calculate the direction of the rod from the given angles.
2. Compute the cross-product of the velocity and the magnetic field vectors.
3. Determine the dot product of this result with the length vector.
4. Use this to find the magnitude of the induced emf.
### Constants and Known Values:
- Length of the rod (\(\mathbf{l}\)) = 27.0 cm = 0.27 m
- Angles of the rod: 39.0° with the x-axis and 51.0° with the y-axis.
- Velocity (\(\mathbf{v}\)) = 6.80 m/s in the +x-direction
- Magnetic field (\(\mathbf{B}\)) = \((0.200 \ \text{T}) \hat{i}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0a59c95-d278-4231-b93f-c228b6025027%2F6d036f1d-1335-460c-adc8-739e47bea1b0%2Faxol47a.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
A metal rod with a length of 27.0 cm lies in the xy-plane and makes an angle of 39.0° with the positive x-axis and an angle of 51.0° with the positive y-axis. The rod is moving in the +x-direction with a speed of 6.80 m/s. The rod is in a uniform magnetic field:
\[ \mathbf{B} = (0.200 \ \text{T}) \hat{i} - (0.280 \ \text{T}) \hat{j} - (0.0900 \ \text{T}) \hat{k} \]
### Part A:
**Question:**
What is the magnitude of the emf induced in the rod?
**Requirement:**
Express your answer in volts.
**Field:**
Electricity & Magnetism
**Equation to use:**
The electromotive force (emf) induced in the rod moving through a magnetic field is given by Faraday's Law of Induction, specifically for a moving conductor:
\[ \mathcal{E} = \mathbf{v} \times \mathbf{B} \cdot \mathbf{l} \]
where:
- \(\mathbf{v}\) is the velocity of the rod,
- \(\mathbf{B}\) is the magnetic field,
- \(\mathbf{l}\) is the length vector of the rod.
### Input Box
```
\mathcal{E} =
[TextInput: 0.00] V
```
**Buttons:**
- Submit
- Request Answer
### Instructions to Students:
To solve this problem:
1. Calculate the direction of the rod from the given angles.
2. Compute the cross-product of the velocity and the magnetic field vectors.
3. Determine the dot product of this result with the length vector.
4. Use this to find the magnitude of the induced emf.
### Constants and Known Values:
- Length of the rod (\(\mathbf{l}\)) = 27.0 cm = 0.27 m
- Angles of the rod: 39.0° with the x-axis and 51.0° with the y-axis.
- Velocity (\(\mathbf{v}\)) = 6.80 m/s in the +x-direction
- Magnetic field (\(\mathbf{B}\)) = \((0.200 \ \text{T}) \hat{i}
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