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The 17.0 cm long rod in the figure below moves at 4.00 m/s. What is the strength (in T) of the magnetic field if a 8.90 V emf is induced

The 17.0 cm long rod in the figure below moves at 4.00 m/s. What is the strength (in T) of the magnetic field if a 8.90 V emf is induced

College Physics
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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The 17.0 cm long rod in the figure below moves at 4.00 m/s. What is the strength (in T) of the magnetic field if a 8.90 V emf is induced?

### Electromagnetic Induction and Lenz’s Law #### Diagram 1: Motion-Induced Electromotive Force The top diagram illustrates the concept of motion-induced electromotive force (EMF) within a magnetic field. It shows a rectangular loop of wire with dimensions ΔA = ℓΔx moving to the right with velocity \( v = \frac{\Delta x}{\Delta t} \). - **Magnetic Field (Bn)**: Represented by crosses (indicating the field is going into the page). - **Current (I)**: Shown as flowing in the loop, driven by the change in the area (ΔA) experiencing the magnetic field. The rectangle's side, ℓ, moves by Δx, thus changing the magnetic flux through the loop, generating an EMF and a current. #### Diagram 2: Application of Lenz’s Law The bottom diagram explains Lenz's Law and its effect on induced current and magnetic fields. - **Magnetic Flux (Φ)**: Increasing as the conducting bar moves to the right. - **Induced Magnetic Field (Bind)**: Opposes the change in flux to satisfy Lenz’s Law, represented by dots (coming out of the page). - **Resistor (R)**: The circuit includes a resistor, illustrating an equivalent circuit with induced EMF (ℰ). Two right-hand rule applications: - **RHR-1**: Determines the direction of force (F) on a moving charge within a magnetic field \( B \) and velocity \( v \). - **RHR-2**: Describes the direction of induced current due to the change in magnetic flux. Overall, these diagrams demonstrate the fundamental principles of electromagnetic induction and the application of Lenz's Law, describing how a moving conductor within a magnetic field generates a current and an opposing magnetic field.
Transcribed Image Text:### Electromagnetic Induction and Lenz’s Law #### Diagram 1: Motion-Induced Electromotive Force The top diagram illustrates the concept of motion-induced electromotive force (EMF) within a magnetic field. It shows a rectangular loop of wire with dimensions ΔA = ℓΔx moving to the right with velocity \( v = \frac{\Delta x}{\Delta t} \). - **Magnetic Field (Bn)**: Represented by crosses (indicating the field is going into the page). - **Current (I)**: Shown as flowing in the loop, driven by the change in the area (ΔA) experiencing the magnetic field. The rectangle's side, ℓ, moves by Δx, thus changing the magnetic flux through the loop, generating an EMF and a current. #### Diagram 2: Application of Lenz’s Law The bottom diagram explains Lenz's Law and its effect on induced current and magnetic fields. - **Magnetic Flux (Φ)**: Increasing as the conducting bar moves to the right. - **Induced Magnetic Field (Bind)**: Opposes the change in flux to satisfy Lenz’s Law, represented by dots (coming out of the page). - **Resistor (R)**: The circuit includes a resistor, illustrating an equivalent circuit with induced EMF (ℰ). Two right-hand rule applications: - **RHR-1**: Determines the direction of force (F) on a moving charge within a magnetic field \( B \) and velocity \( v \). - **RHR-2**: Describes the direction of induced current due to the change in magnetic flux. Overall, these diagrams demonstrate the fundamental principles of electromagnetic induction and the application of Lenz's Law, describing how a moving conductor within a magnetic field generates a current and an opposing magnetic field.
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