The figure below shows a metal bar moving to the right along conducting rails in uniform B- field directed out of the page. Using Lenz's law, determine the direction of the induced magnetic field B in the closed loop defined by the bar and the rails B out to the left to the right out of the page () into the page (x)
The figure below shows a metal bar moving to the right along conducting rails in uniform B- field directed out of the page. Using Lenz's law, determine the direction of the induced magnetic field B in the closed loop defined by the bar and the rails B out to the left to the right out of the page () into the page (x)
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![### Electromagnetic Induction: Determining the Induced Magnetic Field
#### Problem Statement:
The figure below shows a metal bar moving to the right along conducting rails in a uniform magnetic field (B-field) directed **out of the page**. Using Lenz's law, determine the direction of the induced magnetic field (B) in the closed loop defined by the bar and the rails.
#### Explanation of the Diagram:
- **B_out**: The uniform magnetic field directed out of the page is represented by the symbol for vector B with a circle and a dot in the middle.
- **Metal Bar**: The figure includes a metal bar moving to the right, indicated by a red arrow labeled with velocity (v) pointing towards the right.
- **Conducting Rails**: Two parallel horizontal conducting rails form a closed loop with the metal bar.
- **External Circuit**: There is a resistor connected across the rails on the left side.
#### Understanding Lenz's Law:
Lenz's law states that the direction of the induced current (and hence the magnetic field) in a closed loop will be such that it opposes the change in magnetic flux that caused it.
1. **Magnetic Flux Change**: As the metal bar moves to the right, it cuts across the magnetic field lines directed out of the page. This motion changes the magnetic flux through the loop.
2. **Induced Current**: According to Lenz's law, the induced current will flow in a direction that opposes this change in flux.
3. **Direction of Induced Magnetic Field**: The purpose of the induced magnetic field is to oppose the increase in flux due to the bar's motion.
Given the resistor’s orientation, the induced current will create a magnetic field that opposes the direction of the increasing external magnetic field (which is out of the page). Therefore, the induced magnetic field within the loop will be **into the page**.
#### Answer Options:
1. To the left
2. To the right
3. Out of the page
4. Into the page (**selected**)
In conclusion, the induced magnetic field in the closed loop defined by the bar and the rails, according to Lenz's law, is directed **into the page**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc29d20e7-6705-4cf2-a64f-5b2a194784d1%2F23f19ec6-2206-40ad-b369-8d47f739f5d8%2Fx4eju4a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Electromagnetic Induction: Determining the Induced Magnetic Field
#### Problem Statement:
The figure below shows a metal bar moving to the right along conducting rails in a uniform magnetic field (B-field) directed **out of the page**. Using Lenz's law, determine the direction of the induced magnetic field (B) in the closed loop defined by the bar and the rails.
#### Explanation of the Diagram:
- **B_out**: The uniform magnetic field directed out of the page is represented by the symbol for vector B with a circle and a dot in the middle.
- **Metal Bar**: The figure includes a metal bar moving to the right, indicated by a red arrow labeled with velocity (v) pointing towards the right.
- **Conducting Rails**: Two parallel horizontal conducting rails form a closed loop with the metal bar.
- **External Circuit**: There is a resistor connected across the rails on the left side.
#### Understanding Lenz's Law:
Lenz's law states that the direction of the induced current (and hence the magnetic field) in a closed loop will be such that it opposes the change in magnetic flux that caused it.
1. **Magnetic Flux Change**: As the metal bar moves to the right, it cuts across the magnetic field lines directed out of the page. This motion changes the magnetic flux through the loop.
2. **Induced Current**: According to Lenz's law, the induced current will flow in a direction that opposes this change in flux.
3. **Direction of Induced Magnetic Field**: The purpose of the induced magnetic field is to oppose the increase in flux due to the bar's motion.
Given the resistor’s orientation, the induced current will create a magnetic field that opposes the direction of the increasing external magnetic field (which is out of the page). Therefore, the induced magnetic field within the loop will be **into the page**.
#### Answer Options:
1. To the left
2. To the right
3. Out of the page
4. Into the page (**selected**)
In conclusion, the induced magnetic field in the closed loop defined by the bar and the rails, according to Lenz's law, is directed **into the page**.
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