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Consider two infinitely-long current-carrying wires separated by a distance d; one carries current I into the page and one carries current I out of the page. I B I D d

Consider two infinitely-long current-carrying wires separated by a distance d; one carries current I into the page and one carries current I out of the page. I B I D d

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Consider two infinitely-long current-carrying wires separated by a distance d; one carries current I into the page and one carries current I out of the page. (see image attached)

a) Draw the net magnetic field vectors at points A,B,C,D. Only the direction will be graded, not the length. If the magnetic field at the location is zero, indicate that clearly on the diagram.

b) D is located a distance d from both currents. If a particle of charge q is placed at rest at D, what is the magnitude of the magnetic force it experiences, in terms of q, I, d, and/or e0? Explain your answer.

**Title: Analysis of Magnetic Field Between Two Infinitely-Long Current-Carrying Wires** **Introduction:** Consider two infinitely-long current-carrying wires separated by a distance \( d \). One wire carries a current \( I \) into the page, indicated by the symbol \( \otimes \), and the other wire carries a current \( I \) out of the page, indicated by the symbol \( \odot \). **Diagram Analysis:** The diagram illustrates the spatial arrangement of the two current-carrying wires and the points under consideration: 1. **Wire on the Left Side:** - Carries a current \( I \) into the page (\( \otimes \)). 2. **Wire on the Right Side:** - Carries a current \( I \) out of the page (\( \odot \)). 3. **Separation Distance \( d \):** - This is the horizontal distance between the two wires. There are four labeled points around the wires: - **Point A:** Positioned to the left of the wire carrying current into the page. - **Point B:** Located exactly midway between the two wires. - **Point C:** Positioned to the right of the wire carrying current out of the page. - **Point D:** Positioned below the midpoint, at a vertical distance \( d \) from the midpoint \( B \). **Exploring Magnetic Fields:** - **Point A:** - The magnetic field at point A due to the left wire (\( \otimes \)) and the right wire (\( \odot \)) can be determined using Biot-Savart Law or Ampere's Law. - **Point B:** - At this midpoint, the magnetic fields from both wires may exhibit symmetry. The direction and magnitude of the net magnetic field need to be computed by considering the contributions from both currents. - **Point C:** - The magnetic field analysis at point C, similar to point A, considers the influence of both wires. - **Point D:** - This point below the midpoint requires considering the vertical component of the magnetic fields. Understanding these magnetic field interactions is essential in electromagnetism, particularly how the superposition principle applies to magnetic fields generated by currents in different directions. **Conclusion:** This analysis is crucial for comprehending phenomena such as magnetic field lines, forces between current-carrying conductors, and
Transcribed Image Text:**Title: Analysis of Magnetic Field Between Two Infinitely-Long Current-Carrying Wires** **Introduction:** Consider two infinitely-long current-carrying wires separated by a distance \( d \). One wire carries a current \( I \) into the page, indicated by the symbol \( \otimes \), and the other wire carries a current \( I \) out of the page, indicated by the symbol \( \odot \). **Diagram Analysis:** The diagram illustrates the spatial arrangement of the two current-carrying wires and the points under consideration: 1. **Wire on the Left Side:** - Carries a current \( I \) into the page (\( \otimes \)). 2. **Wire on the Right Side:** - Carries a current \( I \) out of the page (\( \odot \)). 3. **Separation Distance \( d \):** - This is the horizontal distance between the two wires. There are four labeled points around the wires: - **Point A:** Positioned to the left of the wire carrying current into the page. - **Point B:** Located exactly midway between the two wires. - **Point C:** Positioned to the right of the wire carrying current out of the page. - **Point D:** Positioned below the midpoint, at a vertical distance \( d \) from the midpoint \( B \). **Exploring Magnetic Fields:** - **Point A:** - The magnetic field at point A due to the left wire (\( \otimes \)) and the right wire (\( \odot \)) can be determined using Biot-Savart Law or Ampere's Law. - **Point B:** - At this midpoint, the magnetic fields from both wires may exhibit symmetry. The direction and magnitude of the net magnetic field need to be computed by considering the contributions from both currents. - **Point C:** - The magnetic field analysis at point C, similar to point A, considers the influence of both wires. - **Point D:** - This point below the midpoint requires considering the vertical component of the magnetic fields. Understanding these magnetic field interactions is essential in electromagnetism, particularly how the superposition principle applies to magnetic fields generated by currents in different directions. **Conclusion:** This analysis is crucial for comprehending phenomena such as magnetic field lines, forces between current-carrying conductors, and
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