Two long parallel conducting wires carry current I1= 1.5 A into the page and unknown current I2 out of the page. The two wires are 1.0 m apart and located on x-z plane as shown in the figure below. a) What is the magnitude of I2 if the net magnetic field at the origin (0,0) is 1.0 µT pointing downward? b) Find out the location (x,y) where the net magnetic field B becomes zero.
Two long parallel conducting wires carry current I1= 1.5 A into the page and unknown current I2 out of the page. The two wires are 1.0 m apart and located on x-z plane as shown in the figure below. a) What is the magnitude of I2 if the net magnetic field at the origin (0,0) is 1.0 µT pointing downward? b) Find out the location (x,y) where the net magnetic field B becomes zero.
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Two long parallel
a) What is the magnitude of I2 if the net magnetic field at the origin (0,0) is 1.0 µT pointing downward?
b) Find out the location (x,y) where the net magnetic field B becomes zero.
![## Magnetic Field Due to Parallel Conducting Wires
### Problem Statement:
Two long, parallel conducting wires carry current \( I_1 = 1.5 \, \text{A} \) into the page and unknown current \( I_2 \) out of the page. The two wires are 1.0 m apart and located on the x-y plane as shown in the figure below.
[Answer in 2 significant figures]
#### Diagram Explanation:
In the diagram, there are two wires:
- Wire carrying current \( I_1 \) is located at x = -0.5 m and the current is directed into the page.
- Wire carrying current \( I_2 \) is located at x = +0.5 m and the current is directed out of the page.
The origin (0,0) lies midway between the wires at y = 0.
#### Questions:
a) **Find the magnitude of \( I_2 \) if the net magnetic field at the origin (0,0) is \( 1.0 \, \mu T \) pointing downward.**
b) **Determine the location (x,y) where the net magnetic field \( B \) becomes zero.**
### Detailed Analysis:
1. **For part (a):**
- The magnetic field due to a long straight conductor at any point is given by \( B = \frac{\mu_0 I}{2 \pi r} \).
- Calculate the individual magnetic fields due to \( I_1 \) and \( I_2 \) at the origin and apply vector addition to determine the net magnetic field.
- Use the given net magnetic field to solve for \( I_2 \).
2. **For part (b):**
- Set up the equation with the condition that the sum of magnetic fields due to \( I_1 \) and \( I_2 \) equals zero at a certain point (x,y).
- Solve for the coordinates (x,y).
This problem investigates the interaction between magnetic fields due to parallel currents and involves applying the right-hand rule and principles of vector addition to solve for unknowns.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb529b68-3495-4a4f-837a-ddb8b824decf%2Fad33973e-2a85-45d6-9502-48f8bd991837%2Fffsrkpu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Magnetic Field Due to Parallel Conducting Wires
### Problem Statement:
Two long, parallel conducting wires carry current \( I_1 = 1.5 \, \text{A} \) into the page and unknown current \( I_2 \) out of the page. The two wires are 1.0 m apart and located on the x-y plane as shown in the figure below.
[Answer in 2 significant figures]
#### Diagram Explanation:
In the diagram, there are two wires:
- Wire carrying current \( I_1 \) is located at x = -0.5 m and the current is directed into the page.
- Wire carrying current \( I_2 \) is located at x = +0.5 m and the current is directed out of the page.
The origin (0,0) lies midway between the wires at y = 0.
#### Questions:
a) **Find the magnitude of \( I_2 \) if the net magnetic field at the origin (0,0) is \( 1.0 \, \mu T \) pointing downward.**
b) **Determine the location (x,y) where the net magnetic field \( B \) becomes zero.**
### Detailed Analysis:
1. **For part (a):**
- The magnetic field due to a long straight conductor at any point is given by \( B = \frac{\mu_0 I}{2 \pi r} \).
- Calculate the individual magnetic fields due to \( I_1 \) and \( I_2 \) at the origin and apply vector addition to determine the net magnetic field.
- Use the given net magnetic field to solve for \( I_2 \).
2. **For part (b):**
- Set up the equation with the condition that the sum of magnetic fields due to \( I_1 \) and \( I_2 \) equals zero at a certain point (x,y).
- Solve for the coordinates (x,y).
This problem investigates the interaction between magnetic fields due to parallel currents and involves applying the right-hand rule and principles of vector addition to solve for unknowns.
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