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his time the magnetic field maintains a constant value of 0.460 T, and we achieve an induced voltage of 0.055 V over a time period of 1.36 s by keeping the magnetic field fixed but changing the area of the wire loop from its initial value of 0.410 m^2. What is the final value of the loop s area after this time period? 0.458 m^2 0.688 m^2 0.573 m

his time the magnetic field maintains a constant value of 0.460 T, and we achieve an induced voltage of 0.055 V over a time period of 1.36 s by keeping the magnetic field fixed but changing the area of the wire loop from its initial value of 0.410 m^2. What is the final value of the loop s area after this time period? 0.458 m^2 0.688 m^2 0.573 m

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College Physics
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Publisher:Raymond A. Serway, Chris Vuille
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4. This time the magnetic field maintains a constant value of 0.460 T, and we achieve an induced voltage of 0.055 V over a time period of 1.36 s by keeping the magnetic field fixed but changing the area of the wire loop from its initial value of 0.410 m^2. What is the final value of the loop s area after this time period?

   
0.458 m^2
   
0.688 m^2
   
0.573 m^2
   
0.229 m^2
### Explanation of Diagram: Magnetic Field Induced by a Current-Carrying Loop This diagram illustrates the concept of a magnetic field generated by a current-carrying loop placed in an external magnetic field. Here is a detailed breakdown of the image: 1. **Loop of Wire**: - The central feature of the diagram is a circular loop of wire, through which an electric current (I) flows in a clockwise direction, as indicated by the purple arrow. 2. **Magnetic Field (\( \mathbf{B}_{\text{out}} \))**: - Small green dots represent the external magnetic field (\( \mathbf{B}_{\text{out}} \)) which is directed out of the page. This indicates the vector field lines pointing towards the viewer. 3. **Magnetic Field Orientation**: - The external magnetic field is uniform across the plane of the loop, as shown by the evenly spaced green dots. ### Educational Context: When a conducting loop is placed in a magnetic field and an electric current flows through it, the interaction between the magnetic field and the electric current induces electromagnetic forces. The right-hand rule can be applied here to determine the magnetic field direction generated by the current, which influences how the loop will interact with the external magnetic field. - **Applications**: Understanding this principle is fundamental in the study of electromagnetism, influencing the design and operation of electric motors, generators, transformers, and other electromagnetic devices. This diagram is useful for visualizing the basic electromagnetic principles governing how currents and magnetic fields interact, forming a cornerstone of electric and magnetic theory.
Transcribed Image Text:### Explanation of Diagram: Magnetic Field Induced by a Current-Carrying Loop This diagram illustrates the concept of a magnetic field generated by a current-carrying loop placed in an external magnetic field. Here is a detailed breakdown of the image: 1. **Loop of Wire**: - The central feature of the diagram is a circular loop of wire, through which an electric current (I) flows in a clockwise direction, as indicated by the purple arrow. 2. **Magnetic Field (\( \mathbf{B}_{\text{out}} \))**: - Small green dots represent the external magnetic field (\( \mathbf{B}_{\text{out}} \)) which is directed out of the page. This indicates the vector field lines pointing towards the viewer. 3. **Magnetic Field Orientation**: - The external magnetic field is uniform across the plane of the loop, as shown by the evenly spaced green dots. ### Educational Context: When a conducting loop is placed in a magnetic field and an electric current flows through it, the interaction between the magnetic field and the electric current induces electromagnetic forces. The right-hand rule can be applied here to determine the magnetic field direction generated by the current, which influences how the loop will interact with the external magnetic field. - **Applications**: Understanding this principle is fundamental in the study of electromagnetism, influencing the design and operation of electric motors, generators, transformers, and other electromagnetic devices. This diagram is useful for visualizing the basic electromagnetic principles governing how currents and magnetic fields interact, forming a cornerstone of electric and magnetic theory.
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