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Suppose the rod is moving with a speed of 6.0m/s perpendicular to a 0.80-T magnetic field. The rod has a length of 1.8 m and a negligible electrical resistance. The rails also have a negligible electrical resistance. The light bulb has a resistance of 96 ohms. Find (a) the e m f produced by the rod and (b) the current induced in the circuit. B X IF X X ++ X XL X (a) x x Conducting rod Conducting rail X

Suppose the rod is moving with a speed of 6.0m/s perpendicular to a 0.80-T magnetic field. The rod has a length of 1.8 m and a negligible electrical resistance. The rails also have a negligible electrical resistance. The light bulb has a resistance of 96 ohms. Find (a) the e m f produced by the rod and (b) the current induced in the circuit. B X IF X X ++ X XL X (a) x x Conducting rod Conducting rail X

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**Electromagnetic Induction in a Moving Conductor** This image illustrates the concept of electromagnetic induction in a moving conductor within a magnetic field. ### Diagram (a) - **Description**: A conducting rod is depicted moving with a velocity \( v \) to the right in a magnetic field. The magnetic field \( \mathbf{B} \) is directed into the plane of the diagram, represented by crosses. - **Explanation**: This setup generates an electromotive force (EMF) across the length \( L \) of the rod due to the motion of the rod in the magnetic field. The positive and negative charges accumulate at the ends of the rod due to the Lorentz force, creating a potential difference. ### Diagram (b) - **Description**: This figure builds upon Diagram (a), illustrating a complete circuit. - A conducting rod is moving to the right on conducting rails while a magnetic field penetrates into the plane. - A hand is shown moving the rod, implying an external force is applied. - The circuit is connected to a light bulb positioned on the left-hand side. - **Explanation**: As the conducting rod moves within the magnetic field, an EMF is induced across its length. The induced current flows through the light bulb, making it glow. The diagram illustrates the relationship between mechanical motion and electrical energy, demonstrating the principle of energy conversion. ### Key Concepts - **Faraday’s Law of Induction**: The diagrams depict how a changing magnetic flux through the loop created by the rail and moving rod induces an EMF. - **Lorentz Force**: The magnetic field exerts a Lorentz force on the moving charges within the rod, leading to the separation of charges and creation of a current in the circuit. These illustrations collectively highlight how relative motion between a conductor and a magnetic field can induce electrical current, a fundamental concept in electromagnetism.
Transcribed Image Text:**Electromagnetic Induction in a Moving Conductor** This image illustrates the concept of electromagnetic induction in a moving conductor within a magnetic field. ### Diagram (a) - **Description**: A conducting rod is depicted moving with a velocity \( v \) to the right in a magnetic field. The magnetic field \( \mathbf{B} \) is directed into the plane of the diagram, represented by crosses. - **Explanation**: This setup generates an electromotive force (EMF) across the length \( L \) of the rod due to the motion of the rod in the magnetic field. The positive and negative charges accumulate at the ends of the rod due to the Lorentz force, creating a potential difference. ### Diagram (b) - **Description**: This figure builds upon Diagram (a), illustrating a complete circuit. - A conducting rod is moving to the right on conducting rails while a magnetic field penetrates into the plane. - A hand is shown moving the rod, implying an external force is applied. - The circuit is connected to a light bulb positioned on the left-hand side. - **Explanation**: As the conducting rod moves within the magnetic field, an EMF is induced across its length. The induced current flows through the light bulb, making it glow. The diagram illustrates the relationship between mechanical motion and electrical energy, demonstrating the principle of energy conversion. ### Key Concepts - **Faraday’s Law of Induction**: The diagrams depict how a changing magnetic flux through the loop created by the rail and moving rod induces an EMF. - **Lorentz Force**: The magnetic field exerts a Lorentz force on the moving charges within the rod, leading to the separation of charges and creation of a current in the circuit. These illustrations collectively highlight how relative motion between a conductor and a magnetic field can induce electrical current, a fundamental concept in electromagnetism.
### Electromagnetic Induction in a Moving Rod Suppose the rod is moving with a speed of 6.0 m/s perpendicular to a 0.80-T magnetic field. The rod has a length of 1.8 m and a negligible electrical resistance. The rails also have a negligible electrical resistance. The light bulb has a resistance of 96 ohms. Find (a) the e.m.f. produced by the rod and (b) the current induced in the circuit. #### Diagrams Explanation: 1. **Diagram (a):** - Shows a conducting rod of length \( L \) moving with a velocity \( v \) perpendicular to the magnetic field \( \mathbf{B} \). - The magnetic field \( \mathbf{B} \) is directed into the plane of the diagram. This is represented by the red crosses. - The velocity \( v \) of the rod is indicated by the rightward arrow. - The conducting rod is shown with a positive and negative sign indicating the direction of the induced e.m.f. 2. **Diagram (b):** - Depicts a complete circuit setup with a conducting rod moving on conducting rails. - The magnetic field \( \mathbf{B} \) is again directed into the plane, indicated by the red crosses. - The rod, as it moves, generates an e.m.f., causing a current to flow through the light bulb, which has a resistance of 96 ohms. - The current's direction is shown flowing from the positive to the negative terminal via the light bulb. #### Calculations: To calculate the e.m.f. (electromotive force) produced by the rod and the current induced in the circuit, we can use the following principles: (a) **e.m.f. (ε):** \[ \varepsilon = B L v \] Where: - \( B = 0.80 \, \mathrm{T} \) (magnetic field strength) - \( L = 1.8 \, \mathrm{m} \) (length of the rod) - \( v = 6.0 \, \mathrm{m/s} \) (velocity of the rod) \[ \varepsilon = 0.80 \times 1.8 \times 6.0 \] \[ \varepsilon = 8.64 \, \mathrm{V} \] (b) **Current (
Transcribed Image Text:### Electromagnetic Induction in a Moving Rod Suppose the rod is moving with a speed of 6.0 m/s perpendicular to a 0.80-T magnetic field. The rod has a length of 1.8 m and a negligible electrical resistance. The rails also have a negligible electrical resistance. The light bulb has a resistance of 96 ohms. Find (a) the e.m.f. produced by the rod and (b) the current induced in the circuit. #### Diagrams Explanation: 1. **Diagram (a):** - Shows a conducting rod of length \( L \) moving with a velocity \( v \) perpendicular to the magnetic field \( \mathbf{B} \). - The magnetic field \( \mathbf{B} \) is directed into the plane of the diagram. This is represented by the red crosses. - The velocity \( v \) of the rod is indicated by the rightward arrow. - The conducting rod is shown with a positive and negative sign indicating the direction of the induced e.m.f. 2. **Diagram (b):** - Depicts a complete circuit setup with a conducting rod moving on conducting rails. - The magnetic field \( \mathbf{B} \) is again directed into the plane, indicated by the red crosses. - The rod, as it moves, generates an e.m.f., causing a current to flow through the light bulb, which has a resistance of 96 ohms. - The current's direction is shown flowing from the positive to the negative terminal via the light bulb. #### Calculations: To calculate the e.m.f. (electromotive force) produced by the rod and the current induced in the circuit, we can use the following principles: (a) **e.m.f. (ε):** \[ \varepsilon = B L v \] Where: - \( B = 0.80 \, \mathrm{T} \) (magnetic field strength) - \( L = 1.8 \, \mathrm{m} \) (length of the rod) - \( v = 6.0 \, \mathrm{m/s} \) (velocity of the rod) \[ \varepsilon = 0.80 \times 1.8 \times 6.0 \] \[ \varepsilon = 8.64 \, \mathrm{V} \] (b) **Current (
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