Two wires carry currents of 20 A each in opposite directions suspended horizontally parallel to each other 55 cm apart. posts supporting these wires divide the lines into straight segments, what magnetic force (direction and magnitude) e oach cegmont 2 Show, a diagram of curronts and forces rrents and forces
Two wires carry currents of 20 A each in opposite directions suspended horizontally parallel to each other 55 cm apart. posts supporting these wires divide the lines into straight segments, what magnetic force (direction and magnitude) e oach cegmont 2 Show, a diagram of curronts and forces rrents and forces
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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![### Problem 5:
Two wires carry currents of 20 A each in opposite directions and are suspended horizontally parallel to each other, 55 cm apart. If the vertical posts supporting these wires divide the lines into straight 10 m segments, what magnetic force (direction and magnitude) is exerted on each segment? Show a diagram of currents and forces.
### Explanation:
This problem involves calculating the magnetic force between two parallel currents. According to Ampère's force law, the magnetic force per unit length between two parallel wires carrying currents \(I_1\) and \(I_2\) separated by a distance \(r\) is given by:
\[ F/L = \frac{\mu_0 I_1 I_2}{2\pi r} \]
Where:
- \(F\) is the force,
- \(L\) is the length of the wire segment,
- \(\mu_0\) is the permeability of free space (\(4\pi \times 10^{-7} \, \text{N/A}^2\)),
- \(I_1\) and \(I_2\) are the currents (20 A each in this case),
- \(r\) is the separation distance (0.55 m).
Determine the total force by multiplying the force per unit length by the length of each segment (10 m).
### Diagram Description:
The diagram should illustrate two parallel lines representing the wires:
1. Label each wire with the current direction.
2. Show the separation distance between the wires as 55 cm.
3. Indicate the magnetic force's direction, which will be attractive if the currents are in opposite directions (as specified, "in opposite directions").](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ebc0c1f-e5f3-4d9b-b90d-7e96848b4de4%2F48f0d526-1e14-4501-8a41-349703c0418d%2Fh8rigbh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 5:
Two wires carry currents of 20 A each in opposite directions and are suspended horizontally parallel to each other, 55 cm apart. If the vertical posts supporting these wires divide the lines into straight 10 m segments, what magnetic force (direction and magnitude) is exerted on each segment? Show a diagram of currents and forces.
### Explanation:
This problem involves calculating the magnetic force between two parallel currents. According to Ampère's force law, the magnetic force per unit length between two parallel wires carrying currents \(I_1\) and \(I_2\) separated by a distance \(r\) is given by:
\[ F/L = \frac{\mu_0 I_1 I_2}{2\pi r} \]
Where:
- \(F\) is the force,
- \(L\) is the length of the wire segment,
- \(\mu_0\) is the permeability of free space (\(4\pi \times 10^{-7} \, \text{N/A}^2\)),
- \(I_1\) and \(I_2\) are the currents (20 A each in this case),
- \(r\) is the separation distance (0.55 m).
Determine the total force by multiplying the force per unit length by the length of each segment (10 m).
### Diagram Description:
The diagram should illustrate two parallel lines representing the wires:
1. Label each wire with the current direction.
2. Show the separation distance between the wires as 55 cm.
3. Indicate the magnetic force's direction, which will be attractive if the currents are in opposite directions (as specified, "in opposite directions").
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