### 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 left2. To the right3. Out of the page4. 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**.

Answered: Image /qna-images/answer/23f19ec6-2206-40ad-b369-8d47f739f5d8.jpg

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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Concept explainers

Ferromagnetism

Ferromagnetism is a mechanism by which some materials show magnetic properties. Iron and magnetite, an oxide of iron, are two naturally occurring materials that show the property of ferromagnetism. The word ferromagnetism is derived from the Latin name of iron, "Ferrum" as it was the first observed material to show such property. The property of ferromagnetism is shown by only a few substances such as iron, nickel, cobalt, and their alloys. Some transition metals and alloys of rare-earth metals also show ferromagnetism.

Question

### 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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