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Three long wires parallel to the x axis carry currents as shown. If I = 17 A, what is the magnitude of the magnetic field at the origin?
Transcribed Image Text:### Example: Magnetic Field Due to Parallel Currents
In this diagram, we have three long, straight, parallel wires carrying electric currents. The wires are aligned parallel to the x-axis, and their positions are given along the y-axis.
1. **Top Wire:**
- Position: y = 2 meters.
- Current: 4I (flowing in the positive x-direction).
2. **Middle Wire:**
- Position: y = -1 meter.
- Current: 3I (flowing in the negative x-direction).
3. **Bottom Wire:**
- Position: y = -3 meters.
- Current: I (flowing in the positive x-direction).
The x-axis represents the horizontal direction, while the y-axis represents the vertical direction. Arrows indicate the direction of the current flow in each wire:
- The top wire has a current of 4I moving to the right.
- The middle wire has a current of 3I moving to the left.
- The bottom wire has a current of I moving to the right.
This setup can be used to study the magnetic fields generated by current-carrying conductors and their interactions according to Ampère's Law or the Biot-Savart Law. The direction of the magnetic field around each wire can be determined using the right-hand rule.
Understanding this concept is crucial in the field of electromagnetism, which has applications ranging from the design of electric motors to the generation of magnetic fields for scientific research.
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